Great question! I actually commend you on thinking about jumping a car because not only do most people not even know how to do it correctly but 99.9% of people don't actually know what they're doing when they're jumping the car in terms of electricity and physics. So let me go through what happens in a good car and what happens when your battery dies. I hope it'll elucidate everything - this is the way I understand it and I don't pretend to be a physicist, so it could be completely wrong. So in a good car, you have a battery. But what's the battery for? The battery supplies current to the starter, which is of course what starts the car. That's all it does. So when you try to start the car, the electric current flows out of the positive terminal, through the load, and to the negative terminal. This supply of current provides the electricity to the starter. Electrons, of course are flowing the opposite direction. Everything's good.
But now your battery dies. So when you go to start the car, the current no longer flows. So you ask your buddy to jump start the car for you. What's happening there? All your buddy is doing is bypassing your dead battery. He's not charging your battery. I repeat, he's not charging your battery - your alternator does that. Remember, your battery is just to start the car. After the engine is started, the alternator provides the current required to power your car and the battery is no longer needed. So when your buddy's car is running, the battery is basically not doing anything. Now remember your battery is dead so it's basically a piece of junk metal (with toxic chemicals inside). By connecting the positive terminal of your dead battery with the positive terminal of his car, you're bypassing your dead battery. You have two batteries in parallel with each other. Your actual physical positive terminal is just an easy chunk of metal to attach the clips to. You could theoretically attach the red clip anywhere on the circuit prior to the load (the starter). And then you attach the black clip to the negative terminal of your buddy's car and ground it somewhere on your car to complete the circuit. So now when you start your car, the current is flowing from the positive terminal of your buddy's car, through the positive terminal of your dead battery which again is just a piece of metal, through the load, to the negative terminal of your dead battery which is the ground and connected to your chassis, through the jumper cable which is connected to some metal surface of your car, and back into the negative terminal of the good battery.
Electrons, of course, move the other way. To illustrate, consider it like this. You can think of the chassis as an electron source for all of this. The electrons move from there via the negative terminal of your dead battery through the load to the positive terminal of your battery to the positive terminal of the good battery to the negative terminal of the good battery back through the cable to the chassis of your car and thus completing the circuit. This bypasses whatever is between the positive and negative terminals of your dead battery, which is what caused it to die.
So usually if your battery isn't holding charge (i.e. you're not just leaving your lights on, etc. when the car and thus alternator is off), the issue is what's between the positive and negative terminals of your battery, i.e. inside your battery. And so you'll need a new one. It's not fixed just because your buddy jumped your car.
Note of caution: never attach the red to black and black to red. This will kill both batteries - sometimes violently.