It refers to the state of being curious, or a strong desire to know or learn something.
Here are some examples:
* Her curiosity led her to ask many questions. (Curiosity is the subject of the sentence)
* The children's curiosity was piqued by the strange sound. (Curiosity is the object of the preposition "by")
* The detective was known for his sharp curiosity. (Curiosity is a noun modifying the noun "detective")