The base of a system of numerals is the number that determines the place values for numerals in that system. For example, in good old base 10, the decimal system, 234 equals 2 times 100 (10 squared), 3 times 10 (10 to the first power), and 4 times 1 (10 to the 0 power). In base 8, the octal system, on the other hand, 234 equals 2 times 64 (8 squared), 3 times 8 (8 to the first power), and 4 times 1 (8 to the 0 power). So 234 in base 8 is the equivalent of 156 in base 10. Which is highly relevant to calculating your age if you happen to be a tree and want to sound like you're 78 years older than you are.
Here's the thing, though. Any positive integer greater than 1 may be used as a base, and of course you can express any number in any base. Computers are fond of base 2 (binary) and base 16 (hexadecimal, which uses the letters A through F after the digits 0 through 9). Base 12 (duodecimal) has a global following. Its advocates include the Duodecimal Society of America and the Cha-Hinsa Society, which advocates inserting two new numerals, Cha and Hinsa, prior to 10. The duodecimal movement has run into opposition, however, from the grassroots pressure group Ten Means Ten. Other popular bases include base 20 (vigesimal, used by Mayan Indians) and the sexiest numeral system in history, base 60 (sexagesimal, used by ancient Babylonians).
OK, got it? Then go get it.