Correct spelling, explanation: the word exhibit comes from the Latin exhibere, so you can see that it was quite a direct borrowing. In exhibit, the h is generally silent, so the letter is kind of unnecessary, but it’s left unchanged due to the past spelling.

Definition of exhibit:
noun
1. a place to showcase something
We went to the Natural History Museum, and I was impressed by the dinosaur bones exhibit.
verb
1. to showcase something
I bought an art studio where I paint and exhibit all of my most significant works.
2. to manifest something
When my dog was younger he used to exhibit signs of aggression, but with a bit of training, we got him to be very kind and gentle.

Incorrect spelling, explanation: exibit is incorrect as it guides us to an incorrect understanding of the word’s origin. In exhibit – the proper spelling – we can clearly determine how the word was constructed. That it had the prefix ex- and the base word hibere, which changed to hibit in English. If we get rid of the h, the structure of the word is altered so it’s not something that should be done. And for this reason, the word is spelled exhibit.