Tensil strength refers to how much of a load can be applied before it breaks?

More or less yes. Tensile force is a stretching force. Think about fishing line because it is measured in tensile strength as well. Stronger fishing line can hold a heavier load before it breaks than a lighter line. Same applies to bike chain. The engine sprocket is like the fishing reel, the rear sprocket is the fish and the top loop of the chain is the fishing line. Under acceleration, the engine sprocket is trying to pull (tensile force) the chain from the rear sprocket to the front.