Well...
In the real world, you can't really change direction while in midair. You can twist and bend your body and use inertia to turn yourself around even though the minimal friction that air provides doesn't really make for a good support of movement, but that's pretty much it. You can't kick off the air to provide extra movement, and you can't voluntarily slow yourself down. While in midair, only two forces are in effect: Air friction, which slows you down in whatever direction you're moving, and gravity, which speeds up your downward motion. You could make swimming motions to propel yourself forward or slow yourself down, but as air friction is so relatively minimal, so would the speed gain or loss be, so it's safe to ignore this.
In Half-Life, you have much greater control over your movement while in the air. You can speed up a little, and you can slow down almost instantly. You can jump directly upwards, then press forward in the air and land a little in front of your previous position. You can jump forward, then press backwards and stop in midair. And so on. This makes the exploit known as bunnyhopping possible. You can bunnyhop because you can do things that you can't do in the real world.
Why can you do this, though? Well, let's say you have to jump from one platform to another, a task that applies to both the real world and to Half-Life (although you do it a lot more in Half-Life). Both platforms are one by one meter, and there's two meters between them. In the real world, it's a comparatively simple task for somebody who has even the most basic control over his own body: Step back as far as you can, take a running start of one or two steps (there isn't really room for more), then jump. Because you have a lot of experience with how your body functions and what it's capable of, it's very easy to jump two meters (or two and a half to land right in the middle of the platform) with great precision. You can finely tune the forward and upward speed of the jump to get the exact trajectory you need.
This fine control is lacking in Half-Life because of the simplistic controls. You can pick between two forward speeds (walk and run) and a grand total of one upward speed (hit the jump key). So basically, you have two possible forward jumps to choose from, versus the almost infinite variety of jumps you can make in the real world. Needless to say, this could make jumping puzzles unnecessarily frustrating if you didn't have a few extra options. Say you have to make a jump: You're not sure whether a walking jump will carry you the necessary distance, and you're afraid of overshooting the target if you make a running jump. Without air control, you'd have a problem. With air control, you simply make the running jump, then hit backward to stop your forward motion as soon as you're over the spot where you want to land. That's why we have air control in Half-Life (and other first-person shooters), and because air control is pretty illogical by itself, it's hard to guard against exploiting it.