Rhyme is the repetition of the end-sounds of words. Examples include Valerie Bloom's use of "tramp" and "camp" in 'The River', Roger McGough's use of "breath" and "death" in 'Oxygen', and Peter Porter's rhyme of a single-syllable word with a polysyllable, "stars" with "particulars", in 'So, Francis, Where's the Sun?'. Each of these is an example of end-rhyme, which means the rhyme occurs at the end of a line, but rhyme can also happen within a line, where it is known as internal rhyme.
A rhyme on a stressed syllable, as in the examples above, is sometimes referred to as 'masculine rhyme'; its counterpart, feminine rhyme, is made up of a stressed syllable followed by one or more unstressed syllables, such as "fishes" and "wishes" in Charles Causley's 'At the British War Cemetery, Bayeux'.
These near-exact repetitions of end-sounds are known as full rhyme (sometimes as perfect, true or exact rhyme). There are also various forms of near-rhymes (half-rhymes, slant-rhymes, pararhymes), which are not exact repetitions, but are close enough to resonate, as David Harsent's use of "supper" and "blubber" as rhymes in 'Marriage: XVI', or P J Kavanagh's "happy" / "Cavafy" in 'Perfection Isn't Like A Perfect Story'. Further types of rhyme include eye-rhyme, which looks like it should rhyme but doesn't (e.g. through / although), and rime riche, in which the words that rhyme sound identical (e.g. hare / hair).
Rhyme can be used purely for its own sake, because it sounds good, but there may also be further reasons; for example, the form of terza rima has overlapping rhymes that give the poem forward motion, as in George Szirtes' 'Preston North End', each stanza's middle line giving the rhyme for the outer two lines of the next stanza. The "breath" / "death" rhyme, noted above, is not only nice in the ears but resonates because these two concepts are linked, as they are in the poem.