In Morphology (study of morphemes or how morphemes join to form words) a morpheme is the minimal meaningful unit in a language. For example the word 'human', 'legal' 'mortal' are morphemes. A morph is a word segment that represents one morpheme. In another words, a morpheme is an abstract unit of meaning and a morph is formal unit with a physical shape. To make it more clear, morpheme is conceptual and it is the description of what a morph is or does to a word; on the other hand morph is the concrete form of a morpheme.
For example, the morpheme meaning 'negative forming' is represented in adjectives using different morphs such as 'in' as in inhuman, 'il' as in illegal, 'im' as immortal, 'ir' as irregular, 'non' as in non-existent, 'dis' as in dishonest, 'ig' as in ignoble
As the examples above shows, the morpheme meaning 'negative forming' can be given shape by various morphs; though various morphs are used, each morph represents the morpheme 'negative meaning'
Allomorphs are the phonetically variant forms of a morpheme.
Example- 1. The plural morpheme -s/-es is phonologically realized in words cats, dogs and watches as /s/, /z/ and /iz/ respectively. The same morpheme has got different phonetic representation, hence they are the allomorphs of 'plural morpheme -s'
Example-2. The English past tense morpheme that we spell -ed has various phonetic representations. It is realized as /t/as in hiked (after voiceless /k/) realized as /d/in explained (after voiced /n/) realized as /id/in accepted (after either /t/ or /d/)