What is Q-point of transistor?
The quiescent (quiet) point are the values of the voltages and currents of a circuit when no signal is present.

From Wiki:


  The operating point of a device, also known as bias point, quiescent
  point, or Q-point, is the steady-state voltage or current at a
  specified terminal of an active device (a transistor or vacuum tube)
  with no input signal applied.


The choice of Q-point depends on the application and is a crucial part of the design process.  The desired Q-point is an input to the DC bias design equations for the circuit.