What does small signal analysis mean?

Strictly speaking, transistors are very non-linear devices. Bipolar transistors don't amplify at all until the base/emitter voltage rises high enough for the base/emitter junction to be forward biased, and you don't get significant current through a MOSFET until the gate/source voltage approaches the threshold voltage.

However, we can use clever circuits to bias the transistors, which means that fairly large d.c. voltages and currents are applied. The bias conditions hold the transistor at an operating bias pointsuch that the behavior of the transistor is fairly linear over a small range of voltages or currents surrounding the bias point. Large-signal analysis pertains to setting up the bias conditions and deals with the non-linear behavior of the transistor. Small-signal analysis assumes that the transistor is correctly biased and concentrates on the linear behavior for small signals, ignoring the messy non-linear stuff.