Its basically staying ahead of your enemy in a battle. With moves like U-turn, Volt Switch, and Baton Pass you get the chance to check out what your opponent is doing, then switch to the appropriate Pokemon to handle the situation.
For example, I'm in a battle and my opponent hard switches their Pokemon out against mine the turn I decide to use U-turn. I currently have out Bug type Pokemon and they switch in a Fire type Pokemon. Since I used U-turn I now have the opportunity to switch into a Pokemon of my own who can handle the Fire type better. Now instead of them having the advantage over me I have it over them giving me a better chance to win the battle.
That's basically what momentum is.