A phoneme is like a snapshot of a sound, and, as with a photo, a phoneme cannot reveal all the subtleties of the object it represents. For example, the phoneme /er/ is pronounced several different ways. On the West Coast of the U.S., it's likely to sound much like the pronunciation of the letter "r" -- [ti gr] -- while on the East Coast, it's more likely to be pronounced like a short u -- [ti guh]. Therefore, since /er/ is not voiced in only one "correct" way, it is the symbol of a sound voiced in several ways. This is why phonemes are said to be "abstract." Each individual sound that can be made is called a phone, and one phoneme can represent multiple phones. There are many more phones in English than native speakers realize. For instance, most people don't know, and can't particularly tell, that we pronounce /t/ slightly differently in the words top and stop. Linguists recognize and categorize such slight differences, though.
Each pronunciation variation within a phoneme is called an allophone. The phoneme /a/, then, is an abstract symbol representing the allophones in cat, was, ma, and every other way the letter "a" is pronounced in various English words.