Explain me please, why if the set of first-order sentences $\displaystyle \Gamma$ has an infinite model, then the set (class) of all models of $\displaystyle \Gamma$, $\displaystyle Mod(\Gamma)$, is strictly bigger than any set $\displaystyle X$?

Here is a passage from a textbook:

... $\displaystyle Mod(\Gamma)$ is sometimes unbounded. It is unbounded precisely when $\displaystyle \Gamma$ has an infinite model. Byunboundedwe mean that for any set $\displaystyle X$, $\displaystyle Mod(\Gamma)$ is strictly bigger than $\displaystyle X.$ ...