The story
Jayus is Indonesian slang, and nobody is quite sure where it comes from. Dictionaries give two senses. As an adjective it simply means lame, failing to be funny. As a noun it is the joke so unfunny, and so badly told, that you laugh anyway.
The second sense is the one that made the word known abroad, through lists of words other languages lack. In Indonesia the two run together, which is part of the fun: whoever calls a joke jayus is often already laughing. A related piece of slang is garing, literally dry and crisp, for a joke that falls flat.
English has the groaner and the dad joke, and both describe the joke itself. Jayus also describes what the joke does to you. First you groan, and then you laugh, half against your will. English has no name for that second moment, the laugh the joke did nothing to earn.
A scene: a birthday party in Bandung. An uncle tells the same pun about a chicken for the third time that afternoon, and laughs at it hardest himself. There is a pause around the table. Then his niece starts to giggle, and the rest follow. 'Jayus,' she says, and it sounds almost like a compliment.