Hexadecimal or base 16 is a number system which uses the numerals 0-9 and letters A-F or a-f to represent digits. It is commonly used in ROM hacking, since it provides an easy way to write the binary numbers used by computers. Often representing numbers as decimal is either unwieldy and meaningless in the case of pointers or obscures the meaning of data stored in bits. For example, a byte could be used as eight true/false flags, but reading the same byte as a decimal number would be meaningless.
More non-ROM hacking specific information can be found at Wikipedia's hexadecimal article.