I found this definition in the dictionary
Allomorph: Any of the variant forms of a morpheme. For example, the phonetic (s) of cats (kts), (z) of pigs (pgz), and (z) horses (hôrsz) are allomorphs of the English plural morpheme
This is also an elaboration for more clarification
A morph is simply the phonetic representation of a morpheme - how the morpheme is said. This distinction occurs because the morpheme can remain the same, but the pronunciation changes.
The best example of this is the plural morpheme in English '-s'. '-s' is the morpheme, but the morph changes in different words:
Cats - '-s' morpheme is pronounced /s/
Dogs - '-s' morpheme is pronounced /z/
Houses - '-s' morpheme is pronounced /ɪz/
These various pronunciations are the morphs of the morpheme '-s'.
This leads onto what an allomorph is. Allomorphs are the varieties of a morpheme, which is closely related to the morph. The morph is just how you pronounce the morpheme, the allomorph is the variation in pronunciation.
So, the morpheme '-s' (plural) has three allomorphs with the morph /s/, /z/, and /ɪz/.
I hope that's clear.
:)