In spoken language, a phoneme is a basic unit of one sound that can change the meaning of a word. A phoneme may well represent several similar sounds.
When writing about phonemes, it is common to use 'slash' markers as quotes around the sound. For example, the phoneme for the initial sound in the word "phoneme" would be written as /f/...
Examples of phonemes in the English language would include sounds from consonants like /p/ and /b/ or combined letters like "sh" or "ch".
Phonology studies the system of phonemes of a language.
What may be an allophone (a different sound belonging to the same phoneme) in one language may be a phoneme in another language. In English, for example, /p/ has aspirated and non-aspirated allophones, e.g. aspirated in /pIn/, but non-aspirated in /spIn/. However, in some languages (e.g. Ancient Greek), aspirated /p_h/ was a phoneme distinct from both unaspirated /p/ and /b/.
As another example, there is no distinction between /r/ and /l/ in Japanese, there is only one /r/ phoneme in Japanese, and no /l/ phoneme.