mail on iMac?

Hi guys, this is my first post so be gentle!

I have just taken delivery of my first ever mac, and sa far it crushes my old PC from a great height!

I am having a spot of bother with the mail app though.

When i read my mails and then try to delete them, it goes through the motions, but the next time i open mail all my messages are back and i can't see a way of getting rid of them for good!

Is there a magical hidden setting that i need to activate

all the best
mark.