pH is basically measure a way to measure the number of H+ ions in a solution. The more H+ ions, the more acidic it is.
The H+ ions come from water - which is pulled apart in the solution. The water splits into equal parts H+ (positively charged hydrogen ions) and OH- (negatively charged hydroxyl ions). If there are equal numbers of H+ and OH- ions in a solution the pH is neutral (i.e. 7).
Adding a base to a solution is the same (chemically) as adding OH- ions to a solution. This, in turn, will lower the number of free H+ ions in the solution. The H+ and OH- re-combine to form (neutral) water. This process will raise the pH - towards more basic numbers.