Accepted is the past tense and past participle of the verb "accept". It means:
1. To receive something willingly ("She accepted the gift")
2. To agree to something ("He accepted the job offer")
3. To recognize as true or valid ("The theory is widely accepted")
4. To admit someone into a group ("She was accepted by Harvard")
In slang usage, accepted can mean "cool" or "approved" ("That outfit is accepted")