It means something to the effect of "I've been caught in a lie and can't keep up the act anymore"

The meaning behind the idiom is that "jig" is an old term for a trick, so you're no longer fooling the person.

Cat's out of the bag

A "jig" is a fast lively dance, usually somewhat comical in appearance.

Because jigs were often performed as comic interludes or sketches at the end of plays, the word "jig" started to mean a a piece of entertainment or a "performance."

Eventually, slang-users in Elizabethan England started using "jig" to mean a clever trick or a "con." If you were "playing a jig" on someone, you were fooling them.

"Up" means that the "time for the performance is up" or concluded. The most common way we use "up" to mean finished is in relation to time. When a clock runs out, the time is "up."

Imagine a cup being filled with water. When it reaches the brim (the top), it is full; it can’t take anymore. In the same way, when a situation or a "jig" (a trick) reaches its limit of time or tolerance, it is "up" at the brim.​

In English, we often add "up" to verbs to show that an action is finished 100%. This is known as a "completive particle" in the study of language.

https://www.merriam-webster.com/dictionary/the%20jig%20is%20up

Thanks for asking, it have been quite confusing. Like hello, hello, what can I get you, ouch busted ... 😁

A swede in France.