With the recent release of Thunderbird 8.0 (and possibly 7.0 – I didn’t check), the Mozilla folks have made a small change to the way add-ons are installed from downloaded files. Until the last version, opening the Add-ons page (Tools -> Add-ons) allowed you to install add-ons from downloaded files by clicking a separate Install button. Indeed, this is how most installation instructions for add-ons tell you how it’s done.
Unfortunately, the Install button has disappeared. Instead, there’s a small drop-down menu next to the search button, and in there is a menu item labelled ‘Install add-on from file…’, which is the new replacement. Click the image on the right for a screenshot to help you out.