Yuval's answer is great. A simpler formulation of what he's described is that finite automata cannot count arbitrarily high, and the amount they can count to is bounded by the number states in the automata. More precisely, for an automata to count to $p$, it needs $p+1$ states (one state would be $0$).
This is, in essence, the entire idea behind the pumping lemma: if a string is really long, the finite automata must "forget" how high its counted and start all over again, allowing you to repeat a section over and over without it caring.
Therefore, any regular language that requires counting to 3 to validate a word in it, cannot be described by a finite automata of size 3.
Can you think of such a language? (Your professor may also expect you to prove this counting argument, though in my curriculum this understanding of the pumping lemma was taken for granted)