Reps and sets are terms used in weight training exercises. They differentiate between the numbers of lifts that are done in quick succession and the number of times the series is repeated during an exercise session.
A rep, or repetition, is the actual lifting and lowering of a a weight. So if you curl a dumbbell up and down five times without stopping, you have performed five reps of that particular arm exercise.
A set is a group of reps separated by time intervals. For example, a completed round of 10 arm curl reps is considered a set of 10. Typically, additional sets will be performed a short time after the first set has been completed.
If the weight trainer wants toned muscles, she should do a higher amount of reps per set. Twelve to 15 reps with a relatively light weight load is typically a successful route to toning muscle.
To build the mass of the body, fewer reps should be performed with heavier weights. The number of sets should depend on how much weight the lifter can handle. In other words, each set should increase the weight amount a little more, and once the lifter cannot reach his usual number of reps, he has reached his maximum weight.
The "reps and sets" terminology may be used in exercises without weights as well, though it is not as common. If you are doing 20 pushups, three times in a row, you may refer to this exercise as three sets of 20 reps.