Transistor at left
This is called "push pull output configuration" and provides unity voltage gain but significantly low output impedance and high output current. This makes push/pull output ideal for driving high capacitive loads such as power MOSFET gates at relatively high frequencies when the driver (IC or MCU) cannot source enough current --widely used in switching converters. No need to place two separate resistors.
Note that VCC and Vi should be at the same level for proper on/off switching. If, for example, VCC = 12V and Vi = 5V, this circuit cannot perform its job.
Transistor at right
It is an emitter follower, you will have a hard time driving near VCC or GND to attach further a MOSFET as above.
