When you think of power, what comes to mind?  Is it someone picking up an incredible amount of weight?  Is it a basketball player throwing down a dunk?  Or is it a car doing 200 mph?  Most people get strength and power confused.  You’ll see on tv a lot of times a person picking up a lot of weight and the commentator will say, “look at the power.”  The sport of powerlifting does nothing to settle this confusion as the name of the sport is a misnomer.  In the sport of powerlifting, the goal is to lift as much weight as possible one time in the lifts of the squat, bench press, and deadlift.  Power is actually the product of force and velocity (how quickly a mass can be moved).
The force-velocity curve us a curve on a graph that tells us the lighter a weight is the faster we can move it and the heavier a weight is, the slower the weight will move.  Since power is a fast movement and heavier weights move slower, the sport of powerlifting a s strength sport and not a power sport and when someone lifts a heavy object, they are displaying strength and not power.  For optimal health and the ability to do activities of daily living such as getting up out of a chair, walking up stairs, or standing up from a kneeling position, all portions of the force-velocity curve need to be trained which means not only heavy lifting for low reps but also lighter loads moved faster.
When most people think of power training two things come to mind: athletes and injuries.  They think athletes are the only people that need power training and the performing power training will lead to injuries.  These two ideas are completely false.  Everyone needs power training.  Power training is taking advantage of the stretch-shortening cycle of the body.  Our muscles are connected by fascia (general term for connective tissue).  As this muscle is stretched, elastic energy is built up (think of stretching a rubber band).  If this energy is not released immediately, the elastic energy is dissipated as heat.  If this energy is released immediately, it contributes to producing more force and faster force.  There are three places where this energy is stored and utilized, in the tendons of muscles, the fascia surrounding muscles, and in the muscles themselves.
There are three phases to a movement: the eccentric (where the muscle is lengthening), the concentric (where the muscle is shortening), and the amoritization phase (the brief period between the eccentric phase and the concentric phase.  The amoritization phase should be very brief in order to not lose that elastic energy as heat and use it for movement.  Think of a basketball player performing a jump shot.  They drop down into a squat first before jumping up to take the shot.  They drop down build up that elastic energy in order to jump higher on their jump shot and achieve more height on the shot.  If they were to stand and shoot, they would have to use far more arm strength in order to achieve the same effect.  When we walk, our legs and arms create a stretch in the fascia when builds up elastic energy to help us walk more efficiently so we are able to walk for long periods of time without getting tired.
Older adults are need power training just as much, if not more so, than younger individuals.  As adults get older, their ability to produce muscular power decreases earlier and sharper than does strength or endurance.  Ask any older adult what their biggest fear is and they will say falling.  Research has shown that power is a bigger determinant of falls than strength.  Elderly fallers in communities and nursing homes have been shown to have less lower limb power than have nonfallers.  Lower limb power is an early indicator of balance deficits and fall risk, even in nonfrail adults.  When there are threats to balance (narrowed base of support, loss of vision, instability), rapid responses must be engaged to maintain balance.  With aging, slowed response initiation further reduces the possible time to produce movement.  As stated earlier, high velocity resistance (power) training results in more robust adaptations in muscle power than does lower velocity (strength) training.
A study by Orr and colleagues took 112 community-dwelling healthy older adults (average age of 69 years old) and split them up into four groups (low, medium, high strength training, and a control group).  The low group used 20% of their 1 repetition maximum (how much weight they can lift 1 time on their own without help).  The medium group used 50% of their 1 RM, and the high used 80% of their 1 RM.  The training program was 8-12 weeks long and the participants trained twice per week.  They performed five exercises for three sets of eight repetitions with a fast concentric and a slow eccentric.  Balance, muscle performance (strength, power, endurance, contraction velocity), and body composition were measured.  They found that power training significantly improved balance (with low intensity power training leading to the greatest improvements in balance) and contraction velocity at low loads leading to being able to predict improvements in balance following training.  Hazell and colleagues in their review found that standard resistance training is optimal for increasing strength in older adults, but power training (that contains high-velocity contractions) is an optimal means of training for older adults in order to increase the performance of activities of daily living.  It is clear from these two studies, as well as many that have supported these two studies, that power training is vital for older adults.  Those that are not athletes or older adults benefit from power training as well.
Power training utilizes more muscle fibers.  Muscle fibers are classified as fast and slow twitch.  Slow twitch muscle fibers are the first muscle fibers activated and are used for picking up light objects and performing movements of long and submaximal duration (walking or sitting for a long period of time), while fast twitch muscle fibers are responsible for lifting a very heavy weight and moving quickly.  Power training (even though it is relatively light) uses the fast twitch muscle fibers without needing to use the slow twitch fibers first.  Power training also increases the efficiency at which the motor units activate which increases the speed at which the muscle fibers contract.  Power training leads to stronger and more resilient connective tissue which reduces the likelihood of injury (sprains and strains).  The hormones that build muscle tissue and burn body fat are also increased in response to power training.  All of these benefits from power training means a stronger and leaner person.
There are many ways to increase power including Olympic weightlifting and plyometrics.  Just because these are two of the best ways to increase power does not mean that they are the only way.  Olympic weightlifting is amazing at increasing total body power but, the movements are highly complex.  This means that they take patience and/or a good trainer to teach you how to perform the movements properly and how to work on the different parts of the lifts.  Plyometrics are phenomenal as well for increasing power development but, if you are afraid of jumping or getting hurt, they are not the best way.  Other means of increasing power is moving your body weight (or a bar, kettlebell, or dumbbell) faster when raising the weight against gravity.  The downfall to this form of speed training is that you spend the last part of the movement slowing down the object to prevent losing control of it.  Another way to increase the contraction velocity of a muscle is to use bands or chains.  This form of training is known as accommodating resistance.
Accommodating resistance takes advantage of the fact that we are weaker when the muscles are stretched and stronger when they are shorter, so there is more resistance in the positions we are stronger in and less resistance where we are at our weakest.  The other benefit to this type of training is that the bands (or chains) naturally pull the object back down so that you don’t have to stop the object yourself.  Medicine balls work really well also for core and upper body power production as well.
Most people think of power training as jumps, Olympic weightlifting, and something reserved for athletes.  This is not the case.  There are many ways to increase power and it offers a multitude of benefits for everybody from young to old and it helps enhance everybody’s life.  Everybody benefits from power training and I highly encourage everyone to program it into their workouts.  The general recommendation for power training is 3-5 sets for 3-8 reps with at least 2 minutes of rest in between sets.  The more reps and the less rest you give yourself means greater fatigue.  Fatigue slows down that movements and it increases the likelihood of injury.

References:
Orr, R., de Vos, N. J., Singh, N. A., Ross, D. A., Stavrinos, T. M., & Fiatarone-Singh, M. A. (2006). Power training improves balance in healthy older adults. The journals of gerontology. Series A, Biological sciences and medical sciences, 61(1), 78–85. doi:10.1093/gerona/61.1.78

Hazell, T., Kenno, K., Jakobi, J. (2007). Functional Benefit of Power Training for Older Adults. Journal of Aging and Physical Activity.15, 349-359. www.journals.humankinetics.com

Häkkinen K. (1989). Neuromuscular and hormonal adaptations during strength and power training. A review. The Journal of sports medicine and physical fitness, 29(1), 9–26.