Bandersnatch: A swift moving creature with snapping jaws, capable of extending its neck. A 'bander' was also an archaic word for a 'leader', suggesting that a 'bandersnatch' might be an animal that hunts the leader of a group.
Beamish: Radiantly beaming, happy, cheerful. Although Carroll may have believed he had coined this word, usage in 1530 is cited in the Oxford English Dictionary.
Borogove: Following the poem Humpty Dumpty says: " 'borogove' is a thin shabby-looking bird with its feathers sticking out all round, something like a live mop." In explanatory book notes Carroll describes it further as "an extinct kind of Parrot. They had no wings, beaks turned up, made their nests under sun-dials and lived on veal." In Hunting of the Snark, Carroll says that the initial syllable of borogove is pronounced as in borrow rather than as in worry.
Brillig: Following the poem, the character of Humpty Dumpty comments: " 'Brillig' means four o'clock in the afternoon, the time when you begin broiling things for dinner." According to Mischmasch, it is derived from the verb to bryl or broil.
Burbled: In a letter of December 1877, Carroll notes that "burble" could be a mixture of the three verbs 'bleat', 'murmur', and 'warble', although he did not remember creating it.
Chortled: "Combination of 'chuckle' and 'snort'." (OED)
Frabjous: Possibly a blend of fair, fabulous, and joyous. Definition from Oxford English Dictionary, credited to Lewis Carroll.
Frumious: Combination of "fuming" and "furious". In the Preface to The Hunting of the Snark Carroll comments, "[T]ake the two words 'fuming' and 'furious'. Make up your mind that you will say both words, but leave it unsettled which you will say first. Now open your mouth and speak. If your thoughts incline ever so little towards 'fuming', you will say 'fuming-furious'; if they turn, by even a hair's breadth, towards 'furious', you will say 'furious-fuming'; but if you have the rarest of gifts, a perfectly balanced mind, you will say 'frumious'."
Galumphing: Perhaps used in the poem as a blend of 'gallop' and 'triumphant'. Used later by Kipling, and cited by Webster as "To move with a clumsy and heavy tread."
Gimble: Humpty comments that it means: "to make holes like a gimlet."
Gyre: "To 'gyre' is to go round and round like a gyroscope." Gyre is entered in the OED from 1420, meaning a circular or spiral motion or form; especially a giant circular oceanic surface current. However, Carroll also wrote in Mischmasch that it meant to scratch like a dog. The g is pronounced like the /g/ in gold, not like gem (since this was how "gyroscope" was pronounced in Carroll's day.
Jabberwock: When a class in the Girls' Latin School in Boston asked Carroll's permission to name their school magazine The Jabberwock, he replied: "The Anglo-Saxon word 'wocer' or 'wocor' signifies 'offspring' or 'fruit'. Taking 'jabber' in its ordinary acceptation of 'excited and voluble discussion', this would give the meaning of 'the result of much excited and voluble discussion'..." It is often depicted as a monster similar to a dragon. In the above old image it has four legs and also bat-like wings. In Alice in Wonderland (2010 film) it is shown with back legs only, and on the ground it uses its wings as front legs like a pterosaur, and it breathes out lightning flashes rather than flame.
Jubjub bird: 'A desperate bird that lives in perpetual passion', according to the Butcher in Carroll's later poem The Hunting of the Snark. 'Jub' is an ancient word for a jerkin or a dialect word for the trot of a horse (OED). It might make reference to the call of the bird resembling the sound "jub, jub".
Manxome: Possibly 'fearsome'; Possibly a portmanteau of "manly" and "buxom", the latter relating to men for most of its history; or "three-legged" after the Triskelion emblem of the Manx peoplefrom the Isle of Man.
Mimsy: Humpty comments that " 'Mimsy' is 'flimsy and miserable' ".
Mome: Humpty Dumpty is uncertain about this one: "I think it's short for 'from home', meaning that they'd lost their way, you know". The notes in Mischmasch give a different definition of 'grave' (via 'solemome', 'solemone' and 'solemn').
Outgrabe: Humpty says " 'outgribing' is something between bellowing and whistling, with a kind of sneeze in the middle". Carroll's book appendices suggest it is the past tense of the verb to 'outgribe', connected with the old verb to 'grike' or 'shrike', which derived 'shriek' and 'creak' and hence 'squeak'.
Rath: Humpty Dumpty says following the poem: "A 'rath' is a sort of green pig". Carroll's notes for the original in Mischmasch state that a 'Rath' is "a species of land turtle. Head erect, mouth like a shark, the front forelegs curved out so that the animal walked on its knees, smooth green body, lived on swallows and oysters." In the 1951 animated film adaptation of the previous book, the raths are depicted as small, multi-coloured creatures with tufty hair, round eyes, and long legs resembling pipe stems.
Slithy: Humpty Dumpty says: " 'Slithy' means 'lithe and slimy'. 'Lithe' is the same as 'active'. You see it's like a portmanteau, there are two meanings packed up into one word." The original in Mischmasch notes that 'slithy' means "smooth and active" The i is long, as in writhe.
Snicker-snack: possibly related to the large knife, the snickersnee.
Tove: Humpty Dumpty says " 'Toves' are something like badgers, they're something like lizards, and they're something like corkscrews. Also they make their nests under sun-dials, also they live on cheese." Pronounced so as to rhyme with groves. They "gyre and gimble," i.e., rotate and bore. Toves are described slightly differently in Mischmasch: "a species of Badger [which] had smooth white hair, long hind legs, and short horns like a stag [and] lived chiefly on cheese".
Tulgey: Carroll himself said he could give no source for Tulgey. Could be taken to mean thick, dense, dark. It has been suggested that it comes from the Anglo-Cornish word "Tulgu", 'darkness', which in turn comes from the Cornish language "Tewolgow" 'darkness, gloominess'.
Uffish: Carroll noted "It seemed to suggest a state of mind when the voice is gruffish, the manner roughish, and the temper huffish".
Vorpal: Carroll said he could not explain this word, though it has been noted that it can be formed by taking letters alternately from "verbal" and "gospel".
Wabe: The characters in the poem suggest it means "The grass plot around a sundial", called a 'wa-be' because it "goes a long way before it, and a long way behind it". In the original Mischmasch text, Carroll states a 'wabe' is "the side of a hill (from its being soaked by rain)".