Phonemes are said to be 'abstract'. What does the term 'abstract' mean in this context?
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.
When we refer the adjective 'abstract' to a phoneme, we mean that the phonemes do not constitute the real sounds of which words are made. A phonemes is usually defined as the smallest linguistic unit which can make a difference meaning when joined to other phonemes. The real sounds are called 'phones'. To understand the difference, the Wikipedia entry in the first link makes you think of the different pronunciation of the K in KIT and SKILL, while the text in the second links below suggests that you think at how different the sounds produced by the letter P in the words PAN and SPAN are.