A sound change which results in the increase in the number of phonemes in a phonological system. Splits tend to be complex affairs which proceed in stages. The following simple example is hypothetical, but not implausible. Suppose a language has long and short allophones of its vowel phonemes. The conditioning factor is the position of the syllable in the word. In final syllables vowels are long. Elsewhere they are short. Take two forms like: /bitə/ and /bit/. These are phonetically [bitə] and [biːt]. Now suppose that the language undergoes a change where final syllables are deleted. The two phonetic forms would now be [bit] and [biːt]. In effect the conditioning factor has disappeared and a new phoneme /iː/ has appeared.
A reasonably simple example from the history of English involves the sounds n and ŋ. It seems likely that these two sounds belonged to the same phoneme with ŋ appearing before velar plosives and n appearing elsewhere. However, some accents dropped final ɡ when it was preceded by ŋ. Thus a pair of words like sin and sing, which used to be sɪn and sɪŋɡ became a minimal pair sɪn, sɪŋ, proving that the two sounds now belong to different phonemes in these accents.