What does pH measure?

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.