The poem "Jabberwocky" appears in Chapter 1 of Lewis Carroll's Through the Looking Glass and What Alice Found There. Alice finds the poem in a book and is unable to read it. She holds it up to a mirror and is able to read the words, but it doesn't help that much because most of the words are "hard to understand." Later she meets Humpty Dumpty, who elucidates the poem by defining some of the words. Carroll had actually written the poem when he was much younger, and he defined some of the words himself. Using a combination of Carroll's and Humpty Dumpty's definitions, one could understand the poem this way:

At four o'clock one afternoon, just when people start broiling things for dinner, the lithe and slimy badger-like creatures were gyrating and boring holes into the grass around the sundial. The shabby-looking birds were flimsy and miserable, and the lost green pigs were making a whistling bellow. The father warns his son to beware of the dangerous creature known as the Jabberwock, and also of the Jubjub bird and the Bandersnatch. The son goes forth with his sword seeking the creature. As he is resting by a tree, thinking in a rough, huffing temper, the Jabberwocky comes towards him through the woods. It makes puffing, bleating, and warbling sounds. The young man draws his vorpal sword and slices through the creature, killing it. He decapitates it and gallops home triumphantly. His father praises him, rejoicing with snorting chuckles. The final stanza repeats the first, indicating perhaps that life has returned to normal for the characters now that the manxome foe would no longer threaten them. (Manxome was one of the words Carroll left no explanation for; vorpal was another.)

Despite the poem's plentiful neologisms (made-up words), it is remarkably clear. Most people can understand the young man's courageous quest and the celebration at his success. Since English is a word-order language, readers can guess what parts of speech the nonsense words are, and their similarity to known words gives a sense of the meaning even before any definitions are given. The poem has been so popular that two of its nonsense words have made it into dictionaries as real words: galumphing and chortle. 

"Jabberwocky" is a nonsense poem by Lewis Carroll, famously appearing in his novel Through the Looking Glass, the sequel to Alice's Adventures in Wonderland. The poem is free to read online, and can be found at eNotes in the links below along with a study guide. Here is a brief summary.

As strange and wonderous creatures (slithy toves, borogoves) perform activities at the time of day called "brillig," a father warns his son about the more dangerous beasts in the forest, most importantly the Jabberwocky. The son, unafraid, takes his "Vorpal Sword" and goes to find the Jabberwocky, intending to kill it. After he searches for a long time, he rests by a tree. By coincidence, the Jabberwocky shows up, and the son engages it in battle. With the power of his sword and his will, he kills the Jabberwocky, and takes its head back with him as proof. His father exults and celebrates, and the creatures mentioned in the first stanza repeat their activities, indicating that at least one day has passed (as it is "brillig" again).

The poem has been interpreted variously as a coming-of-age metaphor, a straightforward heroic ballad (as in Beowulf), or simply as a children's poem full of funny words meant only for amusement.