Rhyme is a dastardly fellow. He's always got something up his sleeve. Some confidence game. Some elaborate plot to take us for all we're worth, move to Florida and live happily ever after.
Oh wait. That's Charles Ponzi.
Rhymes are far less nefarious, although they do scheme. Luckily rhyme schemes result in pleasant music for the ears, rather than empty bank accounts. That's because rhyme schemes are patterns of end rhymes in poems and songs, and they make things sound, well, nice.
'Twas brillig, and the slithy toves
Did gyre and gimble in the wabe;
All mimsy were the borogroves,
And the mome raths outgrabe.
Toves rhymes with borogroves, and wabe rhymes with outgrabe. So the rhymes alternate every other line, making the rhyme scheme of this stanza, ABAB.
Once upon a midnight dreary, while I pondered, wear and weary
Over many quaint and curious volume of forgotten lore—
While I nodded, nearly napping, suddenly there came a tapping,
As of some one gently rapping, rapping at my chamber door—
"'Tis some visitor," I muttered, "tapping at my chamber door—
Only this and nothing more."
Weary and tapping kind of jump out right? That's because they don't end-rhyme with anything else in the stanza. Each of those line endings will get their own letter in the rhyme scheme. But lore rhymes with door, and more. That means they'll all share a letter. They're besties, and besties share. So if we were to write out this rhyme scheme, it would go a little something like this (ahem, ahem): ABCBBB.
As you study poetry, you might find yourself having to figure out a poem's rhyme scheme. Don't panic, and carry a towel. Also, just use your ears. You know, those weird looking things strapped to the sides of your head?
Read the poem out loud. The first line will always always always be A. Always. If the sound at the end of the first line pops up again later in the poem, that line gets an A, too. Keep reading. The next different sound you hear at the end of a line gets a B, and if that sound gets repeated at the ends of other lines, well, then they'll be B's, too. And so on and so forth.
The nice thing is, once you've figured out a rhyme scheme for one stanza of a poem, chances are that rhyme scheme will be repeated in the other stanzas (although that's not a universal truth like, say, that single rich dudes want wives).
For example, sonnets, those pesky little buggers you'll see everywhere you look, are notorious for their more rhyme schemes, which can change, depending on the stanza. And each different type of sonnet has its very own pattern, all it's own. Check 'em out.
To sum up, trust your ears, trust yourselves, and scheme away.