αμαρτία is a noun. The verb is αμαρτάνω. In ancient Greek the meanings were:
αμαρτάνω = αστοχώ (I miss the target)
αμαρτία = αστοχία (miss, failure)
The meaning of the word αμαρτία changed with Christianity: it is the act of braking the law of god by humans.
Here is a very famous ancient Greek quote :
“Το δις εξαμαρτείν ουκ ανδρός σοφού”
Meaning: Making the same mistake twice is not a behavior of a wise man (ie it is not smart to repeat your mistakes).