In linguistics, an allomorph is a variant phonetic form of a morpheme, or, a unit of meaning that varies in sound and spelling without changing the meaning.  The term allomorph describes the realization of phonological variations for a specific morpheme.  The different allomorphs that a morpheme can become are governed by morphophonemic rules. These phonological rules determine what phonetic form, or specific pronunciation, a morpheme will take based on the phonological or morphological context in which they appear. 
English has several morphemes that vary in sound but not in meaning such as past tense morphemes, plural morphemes, and negative morphemes.
For example, in English, a past tense morpheme is -ed. It occurs in several allomorphs depending on its phonological environment, assimilating voicing of the previous segment or inserting a schwa after an alveolar stop: 
The "other than" restrictions above commonly occur in allomorphy: if the allomorphy conditions are ordered from most restrictive (in this case, after an alveolar stop) to least restrictive, then the first matching case usually "win." Thus, the above conditions could be rewritten as follows:
The /t/ allomorph does not appear after stem-final /t/ although the latter is voiceless is then explained by /?d/ appearing in that environment, together with the fact that the environments are ordered. Likewise, the /d/ allomorph does not appear after stem-final /d/ because the earlier clause for the /?d/ allomorph takes priority; the /d/ allomorph does not appear after stem-final voiceless phoneme because the preceding clause for the /t/ takes priority.
Irregular past tense forms, such as "broke" or "was/ were," can be seen as still more specific cases since they are confined to certain lexical items, such as the verb "break," which take priority over the general cases listed above. 
The plural morpheme for regular nouns in English, is typically realized by adding an s or es to the end of the noun. However, the plural morpheme actually has three different allomorphs: [s], [z], and [?z]. The specific pronunciation that a plural morpheme takes on is determined by the following morphological rules: 
The Sami languages have a trochaic pattern of alternating stressed and unstressed syllables. The vowels and consonants allowed in an unstressed syllable differ from those allowed in a stressed syllable. Consequently, every suffix and inflectional ending has two forms, and the form that is used depends on the stress pattern of the word it is attached to. For example, in Northern Sami, there is the causative verb suffix -hit/-ahttit, where -hit is selected when it would be the third syllable (and the preceding verb has two syllables), and -ahttit is selected when it would be the third and fourth syllable (and the preceding verb has three syllables):
There are three allomorphs of the stem: /va:k/, /va:t/ and /va:?/. The allomorphs are conditioned by the particular case-marking suffixes.
The form of the stem /va:k/, found in the nominative singular and locative plural, is the etymological form of the morpheme. Pre-Indic palatalization of velars resulted in the variant form /va:t/, which was initially phonologically conditioned. The conditioning can still be seen in the locative singular form for which the /t/ is followed by the high front vowel /i/.
However, subsequent merging of /e/ and /o/ into /a/ made the alternation unpredictable on phonetic grounds in the genitive case (both singular and plural) as well as the nominative plural and instrumental singular. Thus, allomorphy was no longer directly relatable to phonological processes.
Phonological conditioning also accounts for the /va:?/ form in the instrumental plural in which the /?/ assimilates in voicing to the following /b?/. 
The term was originally used to describe variations in chemical structure. It was first applied to language (in writing) in 1948, by Fatih ?at and Sibel Merve in Language XXIV.