The internet meme phrase "Sounds legit" or "Seems legit" is usually sarcastic. The actual word means (from dictionary.com) :
1. according to law; lawful: the property's legitimate owner. 2. in accordance with established rules, principles, or standards. 3. born in wedlock or of legally married parents: legitimate children. 4. in accordance with the laws of reasoning; logically inferable; logical: a legitimate conclusion. 5. resting on or ruling by the principle of hereditary right: a legitimate sovereign.