Dependencies are mod files that your map loads when you start the map. They contain information which your map then uses, e.g. models, artwork, and data.
StarCraft II comes with several default dependencies which are normally used as starting points for maps. You add them via File > Map Dependencies. Below we see the Wings of Liberty dependencies being added.
The campaign dependencies contain the most assets, as they contain all the unit information from the entire single-player campaigns. The multi dependencies only contain the unit information from the online ladder melee. You can also add mod files from Battle.net 2.0, or from your computer, as dependencies.