Brillig
Carroll’s Explanation:
Bryllyg (derived from the verb to bryl or broil). The time of broiling dinner, i.e., the close of the afternoon.
Humpty Dumpty’s Explanation:
Four o’clock in the afternoon — the time when you begin broiling things for dinner.

Slithy
Carroll’s Explanation:
Slythy (compounded of slimy and lithe). Smooth and active. The proper pronounciation for the word, slithy is slithy with a long “i” (such as in lithe).
Humpty Dumpty’s Explanation:
Lithe and slimy. Lithe is the same as ‘active.’ ... It’s like a portmanteau — there are two meanings packed up into one word.

Tove
Carroll’s Explanation:
Tove, a species of badger. They had smooth white hair, long hind legs, and short horns like a stag; lived chiefly on cheese. “Toves” should be pronounced to rhyme with “groves”.
Humpty Dumpty’s Explanation:
Something like badgers — they’re something like lizards — and they are something like corkscrews. … They make their nests under sundials — also they live on cheese.

Gyre
Carroll’s Explanation:
Gyre, verb (derived from gyaour or giaour, ‘a dog’). To scratch like a dog.
Humpty Dumpty’s Explanation:
To go round and round like a gyroscope.

Gimble
Carroll’s Explanation:
Gymble (whence gimblet). To screw out holes in anything.
Humpty Dumpty’s Explanation:
To make holes like a gimlet.

Wabe
Carroll’s Explanation:
Wabe (derived from the verb to swab or soak). The side of a hill (from its being soaked by the rain.)
Humpty Dumpty’s Explanation:
The grass plot round a sundial ... because it goes a long way before it, and a long way behind it ... and a long way beyond it on each side. (Humpty Dumpty’s explanation was made with some “insights” from Alice.)

Mimsy
Carroll’s Explanation:
Mimsy (whence mimserable and miserable.) Unhappy.
Humpty Dumpty’s Explanation:
Flimsy and miserable.

Borogove
Carroll’s Explanation:
Borogove. An extinct kind of parrot. They had no wings, beaks turned up, and made their nests under sundails; lived on veal. The first ‘o’ in ‘borogoves’ is pronounced like the ‘o’ in ‘worry’. The word is commonly mispronounced as “borogroves”… and this misspelling even appears in some American editions of the book.
Humpty Dumpty’s Explanation:
A thin shabby-looking bird with its feathers sticking out all round — something like a live mop.

Mome
Humpty Dumpty’s Explanation:
I’m not certain about mome. I think it’s short for ‘from home’ — meaning that they’d lost their way.

Rath
Humpty Dumpty’s Explanation:
A rath is a sort of green pig.

Outgrabe
Humpty Dumpty’s Explanation:
Outgribing is something between bellowing and whistling, with a kind of sneeze in the middle.

Most of these definitions were taken from This Jabberwocky Gloassary
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