As you may have notices, this poem includes rhymes.
What might be new to you, though, is how the rhymes are used. Take a look at the following section from the poem:
The children were nestled all snug in their beds, While visions of sugar-plums danced in their heads;
Did you notice that the last words of each line rhymed?
Now, look at the section that follows:
And Mamma in her kerchief, and I in my cap, Had just settled our brains for a long winter's nap.
Again, notice how the last words rhyme with each other.
Now, let's take a look at what happens when the sections are put together:
The children were nestled all snug in their beds, While visions of sugar-plums danced in their heads; And Mamma in her kerchief, and I in my cap, Had just settled our brains for a long winter's nap.