pH is -1 times the logarithm (base 10) of the hydrogen ion concentration
of a compound.  It was originally defined by Danish biochemist 
Soren Peter Lauritz Sørensen in 1909.

In chemistry you often see:

pH = -log[H+] 

where log is a base-10 logarithm and [H+] is the concentration of hydrogen 
ions in moles per liter of solution. According to the Compact Oxford English
Dictionary, the "p" stands for the German word for "power", "potenz", so pH is
an abbreviation for "power of hydrogen".

The pH scale was defined because the enormous range of hydrogen ion
concentrations found in aqueous solutions make using H+ molarity awkward.
For example, in a typical acid-base titration, [H+] may vary from about
0.01 M to 0.0000000000001 M. It is easier to write "the pH varies from 
2 to 13". 

The hydrogen ion concentration in pure water around room temperature is about
1.0 × 10-7 M. A pH of 7 is considered "neutral", because the concentration of
hydrogen ions is exactly equal to the concentration of hydroxide (OH-) ions
produced by dissociation of the water. Increasing the concentration of hydrogen
ions above 1.0 × 10-7 M produces a solution with a pH of less than 7, and the
solution is considered "acidic". Decreasing the concentration below 1.0 × 10-7
M produces a solution with a pH above 7, and the solution is considered "alkaline" or "basic". 

pH is often used to compare solution acidities. For example, a solution of 
pH 1 is said to be 10 times as acidic as a solution of pH 2, because the
hydrogen ion concentration at pH 1 is ten times the hydrogen ion concentration
at pH 2. This is correct as long as the solutions being compared both use the
same solvent. You can't use pH to compare the acidities in different solvents
because the neutral pH is different for each solvent. For example, the
concentration of hydrogen ions in pure ethanol is about 1.58 × 10^-10 M, so
ethanol is neutral at pH 9.8. A solution with a pH of 8 would be considered
acidic in ethanol, but basic in water! 

Edwin