In multiplayer, an Asari can do a teleport-dash using spacebar... but this drains her barrier.
What are some good ways to use this? Does this dash make you immune to certain damage while using it?
It is a big advantage when dodging grenades, missiles or dashing through a room to get away from a banshee or some other large enemy. As @RavenDreamer pointed out you are immune to all damage while dashing, so the splash damage from explosives is no problem.
More in a pvp vein, you can freeze your enemies to break their rhythm dash in a precision kill someone with your beefed up pistol. You can also use this to position yourself for a follow up attack.
If you play a Vanguard you can follow up with Charge to recharge your barrier.
You want to be careful around enemies with strong melee attacks however, since the pause and decreased barrier could be all they need to start tearing you several new holes.