Phonemes are the smallest units of sounds in a language. If a phoneme is changed, the word may change, e.g. change the l sound in 'lack' to a b and the word changes to 'back'.

Example
In English, the sound e in 'pet' and i in 'bit' are examples of vowel phonemes, the sounds j in 'judge' and sh in 'ship' are consonant phonemes. Diphthongs include the oy sound in 'boy' and the ay sound in 'bay'.

In the classroom
Phonemes are the basic building blocks of spoken language. Learners can be helped to discriminate phonemes through comparing 'minimal pairs'; pairs of words which differ only in one phoneme. Another approach is to integrate the teaching of pronunciation, dealing with aspects of pronunciation as they come up, rather than systematically.

See also:
https://www.teachingenglish.org.uk/article/phonemic-script
https://www.teachingenglish.org.uk/article/phonemic-symbols-1
https://www.teachingenglish.org.uk/article/phonology

Further links:
https://www.teachingenglish.org.uk/article/teaching-schwa
https://www.teachingenglish.org.uk/article/speech-language-impairment
https://www.teachingenglish.org.uk/article/same-sound-different-sound
https://www.teachingenglish.org.uk/article/c-consonant-v-vowel
https://www.teachingenglish.org.uk/article/using-phonemic-chart