A statistical model is a formalization of relationships between variables in the form of mathematical equations. The model is statistical as the variables are not deterministically but stochastically related.
In mathematical terms, a statistical model is frequently thought of as a pair $(Y, P)$ where $Y$ is the set of possible observations and $P$ the set of possible probability distributions on $Y$ . It is assumed that there is a distinct element of $P$ which generates the observed data. Statistical inference enables one to make statements about which element(s) of this set are likely to be the true(s) one.