What I mean by compound exercises are those that use a lot of muscle groups, for example the squat both engages your legs and your glutes (bum) but also your core (abs and lower back). Just for completeness an exercise that would not count as a compound exercise is a bicep curl. Now there are advantages to both types of exercises.
Firstly, the single group exercises allow you to specifically target that muscle and make it stronger/bigger. It also allows you to vary your workout as there are many more variants of exercises for single muscle groups than there are compound exercises.
When it comes to compound lifts there are three key lifts that you should try; the squat, the deadlift and the bench press. I highly recommend using these 3 exercises as a way of increasing your overall strength as they incorporate a bunch of different muscle groups at one time.
So why is it important to use multiple muscles at once?
Well the key here is the intensity, see when you go for a jog the intensity is very low so it takes a long time and you don't really get your heart going. With compound exercises your whole body is moving to lift a heavy weight, this means that your whole body is using up your energy stores much faster than any other exercise because the intensity is so high! Meaning you can work out for less time and get more results.
It also means that more of your body is tired at the end of the workout. This is especially important. The more muscles that are tired, the more your body needs to repair itself, this means that your body keeps using up it's stores for hours after you finish your workout. This doesn't mean that you can just go to the gym, destroy your body and then sit around for a couple of days. You have to remember that those stores are there for a reason, and your body will (once you finish using them) start to breakdown something much easier to breakdown, your muscle. So it's important to eat soon after you workout to stop your body from breaking down muscle (which is why so many people bring protein shakes with them to the gym, it stops the muscle from being broken down).
Another benefit of using these big muscle groups together is that these bigger muscle groups cause more growth hormones to be released (especially the legs), which promotes your body to build more muscle.
If you have any questions about this or anything else you would like to ask, please leave a comment and let me know :)