How you chose to lift weights depends on what your training goals are. How you perform the RM repetitions will determine what type of adaptation you get from your workout.
Basically there are four primary reasons to lift weights:
1) for improved strength - being able to lift the heaviest weight possible. Muscular strength is used when lifting or carrying a heavy package, pushing a big gear up a hill on a bicycle, or carrying your child on your shoulders around the amusement park without undue fatigue.
2) for improved appearance - lifting for strength combined with cardiovascular exercise and moderate caloric restriction both required in addition to lifting in order to burn excess body fat.
3) for improved power - being able to lift a weight explosively, as fast as possible. Explosive power is used when hitting a golf ball or soft ball, preforming a tennis serve, or when jumping for a rebound in basketball.
4) for increased size - muscular hypertrophy, or size, training involves specific types of contractions which stimulate growth rather than increased strength or power.
Before getting into how to lift for each goal I first want to define a few terms. Most lifts incorporate three types of muscle contractions.
Isometric contractions are where the muscle contracts but there is no change in joint angle - you are simply contracting the muscle to hold the weight; concentric contractions - where the muscle contracts and the joint angle is reduced and the weight is lifted; and eccentric contractions- where the muscle contracts while lengthening and resisting gravity (or momentum) to return the weight to the starting position.
When training for strength or tone you basically perform each repetition of your RM sets in a slow and controlled fashion both during the concentric (shortening) phase of contraction and during the eccentric (lengthening) phase of contraction. Slow, controlled movement allows you to lift heavy weights and gain strength and tone.
If power is what you desire, be it to improve your tennis serve, golf swing, or vertical jump then RM sets need to be performed explosively in the concentric phase and slow and controlled in the eccentric phase of contraction.
Scientific studies have shown that slow-velocity strength training does little to improve muscle power. Only fast-velocity concentric training improved muscle power. Since the speed of contraction, (only in the concentric phase), needs to be as fast as possible the weights lifted for RM sets will be much lighter than during slow-velocity strength training RM sets.
As an example of this - try doing a curl as fast as possible in the concentric phase with a five pound dumbbell. Next try the same movement with a fifteen pound dumbbell. See how much slower the heavier weight moves and the movement feels? For fast-velocity power training to be effective lighter weights must be used. A weight typically between 20 to 40 percent of one's slow-velocity, strength training RM load.
One note of caution, explosive power training is extremely traumatic on the joints and connective tissue and should be limited to elite athletes after they have developed an appropriate musculoskeletal strength conditioning base fitness level and under proper supervision. Otherwise, power training should be limited to sports-specific training and left out of the weight room.
Finally, to optimize muscle growth when training for size heavy loads must be lifted in the eccentric phase of contraction. Doing forced reps or negative with assistance from a partner allows for heavier weights, than can be lifted in the concentric phase of a lift, to be controlled in the eccentric phase. Since the muscle moves less "efficiently" in the eccentric phase and connective tissue elements aid in controlling the movement and work against gravity, heavier weights can be handled in the eccentric phase. Typically loads which are 120 to 140 percent greater than slow-velocity strength RM loads can be handled in the eccentric phase during forced or negative reps.
No matter what your training goal, proper lifting technique and form are as essential as lifting speed and appropriate load to assure your continued progress and ability to attain desirable adaptations.
With this additional knowledge I hope you have a great weight workout.