One name for the arrangement is a push-pull driver. It is used to provide a low impedance, relatively high current, source and sink to allow the gate capacitance of the MOSFET to charge/discharge quickly. This ensures the MOSFET is either fully 'on' or fully 'off'; not in a half-way state where maximum heat dissipation would occur.
A power MOSFET has a large gate capacitance, so a low impedance driver is needed to rapidly charge and discharge this capacitance, as Alec noted.
The circuit you posted is a push-pull emitter-follower driver.
Google IR (International Rectifier) Power Mosfet manual AN-937
Page 5, Section 4
Gives an explanation of totem pole and other interfaces to Mosfets.
Max.