Correct spelling, definition: when you’re not sure how to spell a specific word in English, always look at its origins. In this case, the etymology shows us that the only right form is crescent because the consonants -s and -c must be adjacent to each other. You can clearly see that the right spelling is crescent, not cresent.

Definition of crescent:
1. adjective, having the shape of a crescent
2. adjective, growing, increasing, or developing
A crescent moon peeped out from behind the clouds.
My powers are crescent.

Idioms with crescent:
Some most commonly used idioms include: crescent moon, crescent-shaped, and crescent wrench.

Incorrect spelling, definition: the only right spelling of this word is crescent. It also originates from Latin crescentum (nominative crescens), the present participle of crescere. As you can see, this form contains two specific consonants: -s and -c, just like today’s spelling. Cresent is just a mistake.