If we limit to a single mode for simplicity (doing so we formally describe a mere harmonic oscillator), a Fock state is of the type |n> with n an integer value. This means that there are n quanta of excitation in the mode. |0> corresponds to the ground state (no excitation). It is different from 0 which is the null vector.
This allows to check that <a†a>=n and Var(a†a)=0, i.e., that measuring the number of particles a†a in a Fock state returns always a definite value with no fluctuation.