"Other" storage represents data that your phone and apps need to use for certain purposes, such as storing your text messages, emails, game save data, facebook cache, etc. The phone is supposed to automatically manage this space to keep it in a reasonable range (as long as your phone has GDR2)
If it's really a problem, clear out your text messages, don't download emails, and uninstall facebook (uninstalling an app should take it's related "Other" data with it) and you'll see the number drop, but only ever so slightly. To be honest with you, 684mb of other is a relatively low number. My 8GB phone seems like to keep around 1.3 gb of "Other" data.