Traffic Collision and Avoidance System.

You see other aircrafts close to you on a display (possibly integrated into either the VSI or the navigation display), and if two aircrafts comes too  close to each other the TCAS will first give you a TA (Traffic Alert) and if the situation still persists an RA (resolution advisory), If you get an RA the TCAS will give you instructions how to avoid the aircraft.

The TCAS communicates with other aircraft's TCAS, so if your advisory is to CLIMB, the other aircraft will get a DESCENT advisory, in that way you will go in different directions.

TCAS is available in many different versions, some has RA abilities some (older) don't  

Take a look on this picture
http://www.airliners.net/open.file/387764/L/

On the Navigation display you can see a couple of white diamonds, they symbolize other aircrafts. +09 means the aircraft is 900ft above you, -20 obviously mean the aircraft is 2000ft below.
Up/down arrows indicates if aircraft is descending or climbing.