To deploy is to move into fighting formation, the way a military commander might deploy troops in preparation for a battle. You'll almost always find the word deploy in a military context.
The Latin plicāre means "fold." By adding dis- to it, to get displicāre, we get the idea of an "unfolding," or distributing. This is the basis of the word deploy, and it gives us a good mental image of the sending out, or "unfolding," of troops in a military plan. To deploy means more than just dispersing troops, however — there is usually a specific formation in mind, consistent with military strategies. And you can deploy nonmilitary assets, too, like accounting teams before an IRS audit.