I am trying to remove a pop up box that appears in the upper right hand corner as in attachment. Please help?

The home page is coming up. If I have incoming e-mails when I try to open them, a pop up box appears in the upper right hand corner. I have to open this box as you would an attachment to a e-mail that has been sent to my computor. This is very annoying. I want to be able to go from my home page to my e-mails without going in box, then the box to open it. I want to be able to read my mail when i open the e-mail feature as well as all others. We have a block on our computer to protect my fifteen year old granddaughter from seeing those things she does not need to see, which by the way does not work either, when I am able to see couples with very little left to the imagination along with ads for viagra and junk. If anyone can help me clean up this mess. Please advise