I have read many answers but I cannot get the basic explanation. There's no need for full details. I just need some basic information about who can create a mac and verify it.
Anyone who holds the key can create a MAC. For any secure MAC it should be computationally infeasible to create a MAC without knowledge of the key.
By the correctness of a MAC, anyone who holds the key can verify it. In pretty much any practical MAC, the key is also needed to verify, but this is not something that's actually implied by the functionality or security definitions.
Given that a secret key was exchanged among some parties any of them can authenticate/verify a message using some MAC implementation in conjunction with the shared key. Typically you would share a key between 2 parties because otherwise you cannot tell who was the sender. However, this is not to be confused with the property of non-repudiation that you get from using a digital signature algorithm because in the case of a MAC, for a given message you cannot tell who generated the MAC (because both parties use the same shared key for the generation).