Finite volume method (FVM) refers to a means of calculating solutions to partial differential equations which is especially suited to fluid dynamics, e.g., hydrodynamics. It divides a volume with a three-dimensional grid into small volumes and uses the divergence theorem to allow tractable calculation to produce good results.
The divergence theorem relates divergence within a volume to flow in/out of the volume. That fact long with the fact that flow in/out of a volume matches that of the volumes to which it is adjacent allow calculations regarding the interfaces to represent rather well the consequences of what happens inside the volume.
FVMs have the advantage that it is relatively easy to deal with volumes of different sizes and shapes, i.e., in an irregular pattern, more easily than others, e.g., a finite difference method.
FVMs are particularly adapted to fluid dynamics because they involve flow of material which would be between the volumes, which is exactly what FVMs deal with. Also, the fact that they can deal with irregular or moving volumes assists in devising ways to handle discontinuities in fluid flow, particularly shock waves.