Well, the small signal analysis tells you how the MOSFET would work in small signal operations. Like for example if you are using it as an amplifier then you have a DC bias voltage with an AC signal superimposed on the DC, the small signal analysis tells you how that small AC signal will be manipulated. In an amplifier this means determining the gain of the amplifier, the input and ouptput resistances, the maximum output voltage etc... The DC analysis is how the MOSFET reacts under pure DC conditions. So at what voltages it is operating in the triode or saturation regions, and how it behaves in those regions. Transient analysis I'm not totally sure what they want, so i'll just say they want to know how the MOSFET will react to transients 😛.
EDIT: see, there are a bunch of characteristic constants associated with any particular MOSFET, and when you do the analysis in lab you are trying to determine what they are so you can model the MOSFET more accurately and understand how it will react under all sorts of conditions.