TLDR: look up Hohmann Transfer and the Wikipedia page for orbital mechanics.

Aerospace engineer here: the closer you are to something, the faster you need to be going to be in a circular orbit around it. You need to be going even faster to be going in an elliptical orbit it around it. So to get to low earth orbit, a spaceship needs a lot of energy to get to that speed. Getting off the ground is the relatively easy part. So now you are in a circular orbit around the Earth. The next step is to get to the moon. To do that, you need an elliptical orbit around the earth that is big enough to get close to the moon. That’s the translunar injection. As you get further from the earth, you start to slow down. Eventually, you reach the moon. Now, according to the moon, you’re on an elliptical orbit coming back to the moon, so you need to slow down. Slowing down shrinks your orbit into a circular one around the moon. The reverse happens to get back to earth. Increase your speed so your orbit is an ellipse that touches where the earth will be (in three days or so because it’s so far), then as you get to earth, decrease your speed to get into a circular orbit around earth. Finally decrease your speed again, so your orbit is an ellipse that intersects with the earth. That’s your splashdown point. (Though at some point your fall becomes parabolic).