This word is a mix ( Sandhi ) of two hindi words Avadh ( Ayodhya ) and Esh (Lord) which means " The Lord of Ayodhya ".
We can refer to Lord Ram or any other king of Ayodhya as Avadhesh.
Awadesh is a kind person. He respects everyone, he can be rude sometimes but is a very kind person at heart. You cannot find anyone like him. If he enters your world, you are really lucky.