Alliteration is the use of the same consonant sounds in words that are near each other. It is the sound, not the letter, that is important: therefore 'city' and 'code' do not alliterate, but 'kitchen' and 'code' do. Strictly, it is alliteration when these same sounds come at the start of the words, or at the start of their first stressed syllable; it becomes consonance when the similar sounds are found in other places within the word.
To the Anglo-Saxons, alliteration was more important than rhyme; Kevin Crossley-Holland's poem 'Translation Workshop: Grit and Blood' enacts the translation of a piece of Anglo-Saxon alliterative verse by moving in and out of strong alliteration, testing its effects. Sean O'Brien's use of alliteration in the opening stanzas of 'Reading Stevens in the Bath' has the effect of separating the two rivers: the flow of the phrase "far / from the furnished banks" contrasts cleverly with the spluttery "poisoned soup of prawns". Anne Ridler's 'Choosing a Name' presents her new-born son "wailing over a world / With walls too wide", the effect of the alliteration here being to link the wailing with the reason for it.