The main purpose is, of course, to provide a mounting location for the anti-torque tail rotor, which not only counters the main rotor, but also allows the helicopter to steer by either increasing or decreasing the tail rotor speed, or altering the pitch of the tail rotor blades (depending on which design you are talking about). The tail rotor is placed so far backwards to take advantage of the principle of leverage, which means that a small rotor can offer enough turning force to counter a large rotor by virtue of its distance from the main rotor hub. But the tail boom also performs the same function as the rear fuselage and horizontal stabilisers on an aircraft too, in that it provides the mounting location for the horizontal stabilisers on a helicopter as well: if you take a close look at the horizontal stabilisers on most helicopters (usually mounted midway down the tailboom), you will see that (like most aircraft) they are basically an upside-down aerofoil section in order to force the tail downwards and provide stability. If you've ever seen gun camera footage of a WW2 plane which has had its tail shot off, it will be apparent why this is necessary!
Chock