Is there any mistake in that sentence?

"Time flies like an arrow." Does it mean time flying or creatures known as "time flies" are like an arrow?

I don't understand that sentence. Is there any mistake in that sentence?

No, that sentence is fine. The subject is "time", and the verb is "flies"; it means that time moves forward at a constant and rapid pace.

This sentence is often found as part of a play on words by Groucho Marx: "Time flies like an arrow. Fruit flies like a banana." (Or in other words "[Time=subject] [flies=verb] like an arrow. [Fruit flies=subject] [like=verb] a banana.")