It is one of the informal ways of saying goodbye to someone. Apparently, this phrase has been derived from a 50's pop song. The person to whom this phrase is being said, says- 'In a while crocodile!'
Mark: See you later alligator!
Janet: In a while crocodile!
by hds2002 December 4, 2015
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This is an old use and still use for this catch phrase to tell someone see you. and the answer for it after while, crocodile, alligator and crocodile were brought for the sake of rhyme.
by Nabeel, January 11, 2008
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A silly way of saying “goodbye,” when you or someone else is leaving. It commands a response... “After while, crocodile.”

Originating in the 1950s, the correct response to “See you later, alligator!” is “After while, crocodile!” It is NOT “In a while, crocodile,” or even “After a while, crocodile.” As with most phrases and expressions, accuracy often gets lost through the years, like a giant game of telephone, so nowadays you will hear it said all three ways, but there is an original, correct way. “AFTER WHILE, crocodile!” :)

*Listen to the song, “See You Later, Alligator,” by Bill Haley and the Comets, for reference.
Bob: “See you later, alligator!”
Jane: “After while, crocodile!”
by MinniebytheSea June 28, 2018
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crocs. That’s it. They’re crocs.
shia LaBeouf could star in these see you later alligator shoes
by urparentsarehot August 19, 2021
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See you later, alligator!“ similar to „See ya!“ is commonly used by single introverts without friends, without a life, without a job and conservative rednecks.
Please never use this.
by Bertholt Brecht November 22, 2021
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