What software have you downloaded recently? Babylon often comes packaged with software downloads from 3rd party software providers. To get rid of it - i'm assuming you use Windows - go to your Control Panel, and look for "Add or remove Programs". Babylon will be lurking in there. Uninstall it. Then double check it is all gone by peeking into your Program Files on your hard drive, usually C drive.
In FireFox, go to "View", and then hover your cursor on "Toolbars" - the items that are checked are what will display in your browser bar.
When downloading and installing new software, be very careful of add-ons and "recommended" software additions. This is how unscrupulous vendors distribute tacky products.