What is a compound lift?
A compound lift is any lift that requires a multi-joint movement to be executed.
The most common examples you will hear are going to be the bench press, squat, deadlift, and overhead press. Though there are other compound lifts, these are the most common four that you will hear about, with the first three being the most common for powerlifting meets.
So what are the benefits?
1A: They burn more calories and get your heart cranking. Incorporating more muscle in a given movement requires that the body use more energy to perform a lift. This is why a squat is going to burn more calories than a bicep curl. Think about how much bigger your legs are than your arms. Now think about the fact that the squat requires activation of the quads, hamstrings, and glutes, unlike the curl, which only really activates the bicep itself.
1B: This also means compound exercises are much more time-efficient. I can burn as many calories and work just as much of my leg muscle as I can with ten sets of squats, as I can combine 20 sets of leg extensions and leg curls, and that doesn't even count the glute work!!
2A: Compound movements elicit a more significant hormonal response from the body. This includes the body's natural release of testosterone and growth hormone in the body. Both of this help facilitate growth and recovery from exercise. Don't fear ladies - it's not enough testosterone to make you get bulky. That would require steroids.
2B: They make you stronger. I challenge you to find two people in the gym regularly—one guy with a fabulous physique, one guy with a meh frame. I guarantee you that the guy with an incredible physique does more compound work. It's 100% best practice for strength training for focus on compound movements.
There are several reasons for this.
Compound lifts allow far heavier loads to be used than non-compound lifts do. If you want to get healthy, you have to lift heavy weights.
Compound lifts elicit a tremendous hormonal and adaptive response more significant than that caused by trying to "add up" some isolation exercises to "sum to" a compound lift.
Compound barbell lifts develop the whole-body coordination necessary to handle heavy weights effectively. Isolation exercises do not. Even if you could make all the muscle groups strong by working them individually, if you have never used them all together as a unit, you will not be able to do so effectively.