The breech is the back end of the barrel that a round goes into before being fired.
I'll try to make sense. Single-action or double-action describes how the hammer or striker is cocked. Although they have "action" in the term, they're not actually describing what kind of "action" the firearm uses. Normally when you talk about a firearm's action, you are referring to the mechanism that loads / ejects rounds.
In blow-back operation, the only thing holding the chamber closed is a spring. When a round is fired, the force of gas pressure pushing the bullet and gases out the front of the barrel pushes the casing and bolt (or slide) to the rear, usually ejecting the case and loading a new round as the bolt (or slide) moves forward again (pushed by the spring).
This works fine for smaller rounds that don't have much power (.22, .380, etc.), but becomes more difficult for larger rounds with higher chamber pressure. Thus, there are other actions like short recoil, gas operated, etc. I won't try to explain all of those here.