Assonance is the repetition of vowel sounds within a short passage of verse or prose. If the repeated sounds are consonants, the figure of speech is consonance when the repeated consonants are in the middle of the word, or alliteration when the repeated consonants are the first letters of the word. A combination of terminal assonance and consonance (the final vowel/consonant combination being repeated) results in rhyme.
Assonance is more a feature of verse than prose. It is used in (mainly modern) English-language poetry, and is particularly important in Old French, Spanish and Celtic languages.