"The Prisoner of Chillon" is a narrative poem written mostly in iambic tetrameter couplets. Before you yawn and click away, let us translate:
A narrative poem is just a poem that tells a story (instead of one like, say, Thomas Hardy's "Afterwards," which is a meditation on death from the poet's own point of view). That's easy enough.
"Iambic tetrameter" describes the meter, or the pattern of stressed and unstressed syllables in each line. The meter is what gives poetry its rhythm, and is the main thing that sets it apart from prose, or regular, everyday language. "Iambic" means that the general pattern is to have an unstressed syllable followed by a stressed syllable: da-DUM. Each "da-DUM" unit is called an "iamb." "Tetrameter" just means that there are four ("tetra") iambs per line. That's all there is to it! Let's look at the meter in action in the first line of the poem:
My hair is grey, but not with years,
If we put the syllables that you'd naturally stress in bold and italics, it would look like this:
My hair | is grey, | but not | with years,
There you have it: four da-DUM units. Four iambs. Iambic tetrameter.
Of course, Byron doesn't make it that easy. He occasionally breaks the iambic tetrameter to insert two shorter lines in iambic diameter (you guessed it: two iambs per line). He does this in lines 2 and 3, but then it returns to the usual tetrameter in line 4:
Nor grew | it white
In a sing|le night,
As men's | have grown | with sud|den fears:
Byron does this again in lines 227-228. What do you think the effect is of these sudden breaks into shorter lines? Does it draw your attention to these particular lines more strongly? Why would he want to do that? What's so important about those lines? Whenever we look in detail at the meter or sound of a poem, it's a good idea to ask ourselves what the effect is of the rhythm. Good poets never do things by accident!
Most of the poem is rhymed in couplets, or in an AABBCCDD pattern. Stanza 11 (lines 300-317), for example, follows that rhyme pattern exactly. Other stanzas, though, have occasional breaks in that general pattern. Look at Stanza 10 (lines 251-299). The stanza starts with ABAB, but then moves into couplets (CCDDEE) until lines 279-282, where Byron uses the ABAB pattern again. Why would he switch back and forth? The interlocking pattern of the ABAB lines suggests that those lines are intimately connected in some way – the pattern forces us to see those lines as a longer, more complicated unit, rather than the shorter units of the two-line couplets. The two sections of Stanza 10 that are ABAB, rather than couplets, are about the speaker's intimate feeling of spiritual connection with the bird that appears at his grate. The interlocking ABAB rhyme pattern could be intended to emphasize that sense of connection.