pH is a measure of the concentration of protons (Hydrogen atoms with no electron) in solution. In a literal sense the p means inverse log of. The H means proton concentration, or [H+].
At pH 5, [H+]= 10^-5 = 0.00001
At pH 6, [H+]= 10^-6 = 0.000001
At pH 7, [H+]= 10^-7 = 0.0000001
At pH 8, [H+]= 10^-8 = 0.00000001
At pH 9, [H+]= 10^-8 = 0.000000001
An acid is a compound that can lose protons. When more protons go into solution, the concentration rises, and the pH lowers (if that makes any sense).
A base is a compound that can pick up protons. When a base goes into solution the number of free protons decrease, and the pH rises.
Alkalinity is the total amount of bases in your water. Most of the base in your water is probably carbonate, so it is essentially a measure of how much carbonate is in the water.