What does "Thanks for having me" mean?

It seems to be used like "Thanks for inviting me". But it sounds like "Thank me, cause I was there".

Looking for a better explanation and situations it should be used in.

You can "have someone for dinner" or "have someone on your show" or "have someone over for coffee" or "have someone in for a chat." In other words, "having someone" means inviting + welcoming + being hospitable.

Thus: "thanks for having me" means thanks for any of those hospitable things. It in no way denotes or implies that the listener should thank the speaker for showing up. "Thanks for" + something is always an expression of appreciation, and never a demand for such.

It can be used in any situation that is friendly and somewhat social. That is, we wouldn't use it in purely business or professional situations.

"Thank you for having me" is a useful parting phrase in social situations where you are a first-time guest or not close to the host. Following it with a compliment is good form.

On radio interview programs, this is the usual response to the host welcoming the guest. The problem with this phrase is that it can sound a bit subservient or insincere. Often the guest is a busy person who is taking time out of his or her schedule to be interviewed. When this is the case, thanks are more logically offered to the guest. A generic "Good to be with you" is gracious without creating the peculiar situation of expressing gratitude to someone who is asking you to do them a favor.