I saw that it is possible to crouch in Alien Swarm, but I didn't really understand its purpose.
Can someone explain it to me?
It's not possible to crouch, it's possible to walk (default binding is shift). When stationary and walking, the animation will show the marine crouched.
The purpose of walk is to be able to move slower when necessary (a rarity in my opinion), and also the minigun is constantly spinned when walking, just like if the alt fire is pressed. Oh, and it looks cool. That's about it.
All this is assuming you don't mean the defensive roll maneuver, which is something else completely, and allows you to evade projectiles (both enemy's and ally's).
EDIT: I've seen some posts in other forums that mention that "crouching" may improve accuracy (i.e. decrease the bullet spread). I've never noticed anything like this, and I browsed the game's source code and it seems that bullet spread does not depend on the stance.
Crouching is achieved by holding down the walk button (
Edit: After @Oak pointed out it didn't work for him, I did some experimenting. It turns out that the effect is so small that it only works when shooting at targets on higher ground. So it's pretty useless, basically.