This poem, for all its whimsy, is mighty regular. "Jabberwocky" is written solely in quatrains (four-line stanzas) that have a regular ABAB, CDCD, EFEF rhyme scheme. The lines themselves are mostly written in iambic tetrameter. That's a lot of syllables, so let's look at the first lines with the accents all marked out:
'Twas brill-ig, and the sli-thy toves
Did gyre and gim-ble in the wabe
Do you notice how there are four stressed syllables in each line, and that they alternate neatly with unstressed syllables, with the unstressed syllable coming first? That's iambic tetrameter for you. The iambic bit refers to the unstressed-STRESSED, unstressed-STRESSED rhythm of it, and the tetrameter bit is just to let you know that there are four iambs (or four unstressed-STRESSED groupings) in each line.
The only irregularity in the rhythm itself is the fact that the last line of each stanza only has three stresses, making it iambic trimeter. (See: "and came ga-lumph-ing back.") But it's still OK to call this poem Ballad Stanza, because ballad stanza isn't the world's most regular form. It can be alternating tetrameter and trimeter, and its rhyme scheme can be ABAB or ABBA or ABCB. It's flexible.
What's a ballad? The short answer is that it's a song. Ballad stanza is traditionally found in folktale songs, and is used as a way for people to communicate legends and tales to each other orally. It's rhythm and rhyme make it easy to remember for this reason. Even though it has some crazy language, "Jabberwocky" is no exception. Because it has the memorable rhythm and rhyme, "Jabberwocky" remains one of the most frequently memorized poems in the English language. Amazing, no?