Bridges combined with the Mainplate form the very foundation of the watch movement. The bridges are used to secure wheels and various other parts in place. After the parts are placed on top of the Mainplate, the bridges are placed on top and screwed against the mainplate, thus securing everything nice and tight.
The more elements that need to be secured with a single bridge, the more challenging it is to set it for the watchmaker.
A balance bridge, is a bridge used exclusively to secure essential bits (balance wheel & spring) of the escapement to the mainplate.