PPA = Personal Package Archive. It's another means for Ubuntu/Mint to upgrade packages that are not in the official repositories.
If you click on your red X, you will open the Update Manager. Click the Edit menu and select Software Sources, give it your root password and click OK. The Official Repositories load first, and from there you can click on the Mirrors for the Main Mint and Ubuntu Base to select differernt Mirrors. On the left, just below Official, you find the PPA's that you may be using. Maybe you aren't using any, but I have 4 in there. Under Additional Repositories, I have two listed, but neither is enabled. Then there are Authentication Keys and a Maintenance option. I don't know if any Maintenance options will help.
But while you're on this screen, in the upper right is a button to Update Sources. I'm pretty sure this is the same as the command line "sudo apt-get update" and it would be good to click and see if it reports any errors to you. It may tell you what is failing... a mirror, a PPA, or whatever.
Also, on the Official Repositories screen, I do not have source code or optional components checked. Unless you know you need them, I would uncheck them if you find them checked. There is a button at the bottom of that screen to Restore Defaults... that might help too, but it might break some updates, like PPA's.
Clear as mud?