While (hopefully) it is a rare occurrence, sometimes you need assistance getting your AR-10/AR-15's bolt open. Maybe a double-feed has resulted from a malfunctioning magazine; perhaps a spent steel case has expanded just a little too much for the extractor to pry it loose; an improperly staked castle nut allowed the buffer tube to work its way loose and the buffer retaining pin pops out, allowing the buffer to come forward and impinge on the bolt; there are a number of things that can go wrong that could cause your AR-15's bolt to require assistance in opening.
Traditionally, the way to clear such glitches is to "mortar" the rifle: strike the buttstock against a hard surface with sufficient force to loosen the bolt carrier group. For many, obvious reasons this is a last-resort effort, as blunt/brute force applied to one's rifle is never a good idea. Fortunately, now there's a better way.
U.S. Tool and Design has come up with a manual bolt extraction device for both the AR-15 and AR-10 platforms. Engineered with precise bolt dimensions, the angled forks allow the tool to be placed at the front of the BCG and lever the bolt open. It's a specialized piece of equipment, but you'll appreciate how simple it makes resolving some mighty complicated problems with the BCG.