Some additional info
While the explantions give are correct, there is some additional information to be aware of. The manual of arms for an open bolt gun is different than for a closed bolt gun. With a closed bolt gun, when the bolt is open, the gun is safe. With an open bolt gun, when the bolt is open, the gun is ready to fire! An open bolt gun with a loaded mag in place and the bolt open is ready to go! Just the opposite of a closed bolt gun!
Open bolt guns are typically submachineguns and machineguns. Select fire rifles (assault rifles and battle rifles) typically fire from the closed bolt. There are a small munber of designs that are exceptions, but generally this is the rule. The BAR (the GI gun, not the civilian sporter rifle) fires from an open bolt, and although called an automatic rifle, it is a light machinegun. The early versions of the BAR were selective fire, but the later versions were full auto only. Another exception is the H&K MP 5, a submachinegun, but it fires from the closed bolt position.
Open bolt guns are not easy to shoot accurate single shots from. The weight of the bolt mechanism going forward to chamber and fire a round is disturbing to precise aiming, and unless mastered with practice, will tend to throw off the shot. With a full auto, this is not a trememdous problem as full autos are seldom used for firing single aimed shots. The throwing off of the aim, and the legal entanglements (open bolt guns are considered by the BATFE as too easy to convert to full auto) are the main reason the open bolt system is not used on semiauto firearms. There used to be a couple of open bolt semi auto "handguns" (the MAC/Cobray for one) but they were taken off the market and redesigned to fire from the closed bolt to get the Feds off their butts. Today they bring outrageously high prices as collector pieces, for what are, in reality, not very satisfactory guns.
The Germans came up with a novel approach with one of their guns, the Falschirmjaegergewehr (paratrooper rifle) the FG 42. A magazine fed 8mm Mauser of very unusual design, and select fire as well. Among a number of unique features is the fact that the FG 42 fired from the closed bolt in semi mode, but when switched to full auto, fires from the open bolt!
Open bolt guns are best to prevent cook off, as the airflow around and through the open chamber helps cool the gun. If you get a cookoff in a closed bolt gun, the correct thing to do is hold on to it (keeping it in a safe - downrange- direction) and drop the mag or twist and break the feed belt (or open the top cover) so the gun runs out of ammo as fast as possible.
In an open bolt gun, when you pull the bolt to the rear, it stays there, and only goes forward when you pull the trigger. I know of an accidental discharge when an undertrained guard loaded his UZI the way he was used to loading his M16! He had to pull the trigger on the UZI to do it, but he got it done!
The safety in an open bolt gun usually does not block the trigger, what it blocks is forward movement of the bolt. There are design exceptions, of course, but blocking bolt movement is the most positive method.
Hope this helps.