What does pH measure?

##pH## is a quantitative measure of the concentration of hydronium ion, ##H_3O^+## in aqueous solution.

Water is known to undergo autoprotolysis according to the following reaction:

##2H_2O(l) rightleftharpoons H_3O^+ + HO^-##

This equilibrium has been exhaustively studied and we write the equilibrium in the normal way,

##K_"eq"=([H_3O^+][HO^-])/([H_2O])##

Because ##[H_2O]## is LARGE, it can be assumed to be constant, and removed from the expression to give:

##K_w=[H_3O^+][HO^-]=10^-14## at ##298*K##

A temperature is specified, because the extent of reaction depends upon temperature, especially for a bond-breaking reaction. Now this is a mathematical expression, the which we can divide, multiply etc., provided that we do it to BOTH sides of the expression. One think we can do is to take ##log_10## of both sides for reasons that will become apparent later:

##log_10K_w=log_10{[H_3O^+][HO^-]}=log_10{10^-14}##

And thus, ##log_10[H_3O^+]+log_10[HO^-]=log_10{10^-14}##

But ##log_10{10^-14}=-14## by definition, and we can rearrange the given expression to give:

##14=-log_10[H_3O^+]-log_10[HO^-]##

Of course, by definition ##-log_10[H_3O^+]=pH## and ##-log_10[HO^-]=pOH##

So for water at ##298K##, ##pH+pOH=14##. This is the defining expression for acid base behaviour in water, and it is one with which you will get very familiar.

So to answer your question (finally!), ##pH## is a quantitative measure of the concentration of ##H_3O^+## (in water).

I apologize for going on so long, but you will need the given background if you don't know it already.