Also, I am having a heck of a hard time understanding the concept of this. No idea why, I just can't seem to understand why I want to fly away from the red planes.
I forgot to answer why you fly away from red planes: In the real world this is called an extension/pitchback fight and is very common (or was very, very common in the F-14 community). Most modern RL fights are E fights so you tend to do one of two things, maximum performance turns (at corner velocity) linked by straight-line extensions for separation and E. You're basically alternating between two maximum performance parameters; best turns and best acceleration. Any time you're not doing one or the other (at least until you have the advantage) is wasting time and E. Airplanes accelerate best when they're not turning and are unloaded to zero G to minimize drag. That means a straight line with the nose being pushed down will give you more speed quicker than anything else at the expense of a bit of altitude. Once you reach your target speed (I usually look for corner up to 300mph) you pull the nose up and start an easy climb to regain the altitude you traded and begin to store that E then do a wingover (the pitchback) and return.
On the other hand, the effectiveness of an extension pitchback depends on how fast you already are, how quickly you can accelerate and what your adversary's plane, NRG state, and position are. The idea is to put as much distance between the two of you as you can while his nose is pointed away from you and then do your pitchback as his nose comes on. Think of it this way. The two of you pass 180 out. You extend building E while he's burning E doing a 180deg turn to follow you. This is why you want to pitchback as his nose begins to point at you, you want him to keep turning and burning E while denying him the ability to build E in a straight line while you've already gained E and did a high-speed pitchback that was more efficient and quicker than his low E turn. If you do this right then you'll be making a series of straight line passes while he's turning small circles to face you.
Another reason for the extension relates to multi-bandit fights. The worst situation for you is when multiple bandits are attacking you from different directions at the same time. A defense against one attack turns your six to another so, you want to do two things. First, isolate the threat sector. There are several ways to do this but one of the easiest is to extend away to position all of the bandits in the same piece of sky which minimizes the possible directions of attack. The other you have less control of but you want to get them attacking you in phase, that means two airplanes attacking from the same direction in the same plane of motion. This makes a defense against one a defense against both. Obviously, you cannot force your adversaries to do this but you can encourage it by being intentionally "predictable".
Here's a grossly oversimplified example. You're in a fight against two adversaries with more E than you have so you turn to pass between them and extend away from them building E while both noses are off you. They see you're extending and think you're trying to escape so they pull hard to come nose on but they're now coming from the same direction, your rear quarter, so you've isolated the threat sector. You now start an easy left turn and they do the same because they both think they're going to get shots on you. This puts them in phase (both are in your rear quarter in an easy left turn and getting closer and closer together as they run you down) and they're probably overconfident (hey, it's 2v1 and they're on your six, what could go wrong?) They're essentially now in a race to see who gets to you first for the kill but at the last moment you use the E you've built to break into them and do a BRD. Since they're in phase they are both presented with the same defense, both overshoot and your BRD is used to convert a 2v1 into a 1v1. Of course, I have to caveat this example. It's not a magic tactic that'll always work because there are just too many variables. How much E difference is there, how maneuverable are they, how far and fast did you get in your extension? The point is that you need to isolate the threat and get them in phase to make your defense much easier. BTW, if they're in phase and together, at attack by you on one of them can easily become an attack on both. I like to appear to be committed to attacking one and then, at the last second, switch to the second who doesn't feel threatened and may be repositioning to attack you if you continue to press your attack on his wingman. It'll quite often catch them by surprise.