I'll explain this with an example:
Musharna vs. Serperior
Serperior used Leaf Blade!
Let's say it does damage but doesn't kill it
Musharna used Trick Room!
Musharna used Psychic!
Since Musharna's speed isn't that great unless you EV train, it becomes faster with Trick Room. So basically, it causes the slower Pokémon in a battle to become faster.
Hope this helps! (-o-)