These are statistical mechanical ensembles, indicating which quantities are conserved; even Wikipedia has decent descriptions of these, and any stat mech textbook will cover them in great detail. The choice of which ensemble you use during data collection depends on what conditions you want to model (e.g. what energy surface you need to sample).
In the microcanonical , or NVE ensemble, the system is isolated from changes in moles (N), volume (V) and energy (E). It corresponds to an adiabatic process with no heat exchange. A microcanonical molecular dynamics trajectory may be seen as an exchange of potential and kinetic energy, with total energy being conserved.
In the canonical ensemble (NVT), amount of substance (N), volume (V) and temperature (T) are conserved. It is also sometimes called constant temperature molecular dynamics (CTMD). In NVT, the energy of endothermic and exothermic processes is exchanged with a thermostat.
In the isothermal–isobaric ensemble, amount of substance (N), pressure (P) and temperature (T) are conserved. In addition to a thermostat, a barostat is needed. It corresponds most closely to laboratory conditions with a flask open to ambient temperature and pressure.
One good and robust strategy when preparing an MD simulation is to run a minimisation, followed by heating and then the actual production run that you are interested in, alternating the ensemble as you go along.
After minimising your solvated receptor-ligand complex, heat it in an NVT ensemble (for example up to 300k), and then start your production in an NPT ensemble with your favourite barostat and thermostat.
It can be a good idea to squeeze in a run of something like 500ps of constant pressure, to equilibrate in the same conditions you want to do your production at, before the production run too. Make sure the backbone RMSD has converged before you move on to the production run.
As Nabeela said above, it is the NPT ensemble that will give you closest resemblance "flask conditions" (and hence make pot-boilers more inclined to glance at your results..) :)
"Constant shape" is not really an ensemble per se, and can be accomplished one of two ways. The first is NVT, but note that you're not just conserving the shape of the box, but the actual box vectors and thus the volume. The box is, by definition, invariant. The second method is NPT with isotropic pressure coupling. The shape of the box will always be the same, but its size (volume) will not be and will oscillate according to the external pressure. The only way the shape changes is if the off-diagonal elements of the pressure tensor are non-zero, i.e. anisotropic pressure coupling.