When are you entitled to assert a conditional $P \to Q$? Precisely when, given $P$ as an assumption, you are in a position to assert $Q$. The natural deduction rule "conditional proof" or "$\to$-introduction" encapsulates that fundamental assumption about the meaning of the conditional. It's an introduction rule because it tells you that when you can argue from $A$ to $C$ you are entitled to discharge the assumption and deduce a proposition $A \to C$ whose main connective is the conditional, thereby introducing a conditional where there wasn't one before.
And the "modus ponens" or "$\to$-elimination" rule is in harmony with introduction rule. For if someone asserts $P \to Q$ they represent themselves as being in a position, given the assumption $P$ to infer $Q$. So if you tell them the assumption $P$ is indeed true, they are committed to $Q$.
You need, contra @rewritten, to clearly distinguish the introduction rule proper (which belongs to a collection of introduction and elimination rules constituting a natural deduction system, for arguing inside a deductive system) from the deduction theorem (which is a meta-theorem which looks at an axiomatic system from outside and says "if there is such-and-such axiomatic proof, then there will also be an axiomatic proof related so-and-so").