Rhyme is not new to us. Nursery rhymes, the most popular types of rhymes, have a certain quality to them — perhaps why we retain them in our memory for longer than we know.
When words are similar sounding in a text, there is a correspondence of sound between words, typically, at the end of lines; when that is the case, we say, they 'rhyme'. These rhyming words make up a rhyme. For example, verse rhymes with curse, terse, worse, purse and so on. These are classic features of verse and/or poems.
For example, the following stanza from Edward Lear's poem The Table and The Chair is a rhyming poem:
Said the Table to the Chair, (a)
'You can hardly be aware, (a)
'How I suffer from the heat, (b)
'And from chilblains on my feet! (b)
'If we took a little walk, (c)
'We might have a little talk! (c)
'Pray let us take the air!' (d)
Said the Table to the Chair. (d)
This poem follows the rhyme scheme aa, bb, cc, dd. This aside, there's more to rhymes; there are types of rhymes, too.