There are two different PM's that you can get. The main one shows up after you log in and then in a yellow box it'll tell you if you have messages. You get to it my scrolling to the top of the page and hit the button about in the middle of the page that says log in. For those you can just push the delete button that is next to the lists of PMs or after you read the message.
The other PM is from the boards and everyone can have free access to it (the first one I talked about you have to be a paid member or pay to receive the PM) But the one situated with the boards you can get to by looking up and to the left. It is right under the words Board index and it's called user control panel. If you click on that it will give you a bunch of tabs one that says messages. (Or you don't even have to go into that section because right next to it there is a thing that says blank new messages and you can click on that to see your messages. )
I hope that helped and didn't confuse you more. Let me reassure you that you did nothing wrong. Everyone gets that message to delete their messages they don't need. If too many get built up then it could bog down the system and make it run slower.
Now if I totally misunderstood you because you asked about deleting your posts which is the things you write on the message boards (like this here is a post) The only way to delete them is if no one else has posted a message under you. If they haven't you can run the mouse over the box and in the right hand corner a little box with an x in it will come up and if you click on that you can delete your posts. Or if someone has posted under you then your only choice is to edit it. But I don't think you're talking about the message boards as that won't bog the siter down and the moderators can delete the posts or threads if need be.
I'm not real computer techie (Personally I think the computers conspire against me to make me even wackier than I am on my own) so I hope this helps answer your question. If not maybe someone who uses words other than doo-hickey can help.