I assume that you understand why these axioms are tautologies (i.e., true under all truth assignments) and that your question is why these were chosen, from among the infinite number of all tautologies, to serve as axioms. Several factors were involved in this choice (I think --- the choice was actually made long before I was around).
First, there was the fairly arbitrary decision to use $\to$ and $\neg$ as the primitive connectives, so that all other connectives ($\land,\lor, \iff$) are viewed as abbreviations. Had other connectives been chosen as primitive, they would have been involved in the axioms.
Second, having included $\to$ among the primitive notions, one has a very simple and widely used (since ancient times) rule of inference, namely modus ponens: From $\phi\to\psi$ and $\phi$, infer $\psi$. The desire to use this rule may well have motivated the choice of $\to$ as one of the primitive notions; the other, $\neg$, may have been motivated as the simplest thing that, together with $\to$, lets you define all the other connectives.
Third, one wants enough axioms to support, with modus ponens, a completeness theorem. That is, every tautology ought to be provable from the axioms using modus ponens. (More generally, every semantic consequence of any set $S$ of formulas ought to be deducible from $S$ and the axioms using modus ponens.) One way to find such a system of axioms is to begin with no axioms, start trying to write a proof of completeness, and gradually add axioms as you see that they are needed for your completeness proof. With extreme good luck, this might lead you to the axioms in the question. With less luck, it will lead you to a messier set of axioms, which you could then try to "clean up" by removing any redundancies, replacing complicated axioms by simpler axioms that imply the complicated ones, etc. I expect that this is how the axioms were first found. Of course, once they're found, people like me don't go through the work of rediscovering them but merely copy them from textbooks.