Fluid mechanics is a branch of physics that describes the behavior of fluids (which include liquids and gases). Fluid mechanics is often considered a branch of continuum mechanics, because fluids are often treated as continuous material, describable with differential equations and tensors.
The central equations for fluid mechanics are the Navier-Stokes equations, which are non-linear differential equations that describe fluid flow. These equations are derivable from conservation of mass and conservation of momentum.
Fluid mechanics is related to statistical mechanics, because fluids can also be modelled as a statistically large number of particles.
The concept of a fluid is surprisingly general. For example, some of the basic mathematics in traffic engineering is derived from considering traffic as a continuous fluid.