This means that the first two lines rhyme (A), the second two lines rhyme (B), and so on. Each stanza has four lines, and the rhyme scheme repeats throughout the poem.
Here's a breakdown of the first stanza:
* Twas the night before Christmas, and all through the house,
* Not a creature was stirring, not even a mouse.
* The stockings were hung by the chimney with care,
* In hopes that St. Nicholas soon would be there.
The words in bold all rhyme.