It can only be used in Briefcase zones. Inside the briefcase, it contains a lot of (possibly fake) U.S. Dollars and it is also equipped with the radio transmitter that will signal other Counter-Terrorists, thus starting the assault.
Once the player reaches a Briefcase zone, the briefcase icon will appear. Select the briefcase, and press the primary fire (MOUSE 1 by default). The player will open the briefcase, revealing the money.
A briefcase also appears in the mission Motorcade Assault in the VIP's safe room. It would seem some unknown individual or group was trying to negotiate with the VIP.