切り refers to a limit, break, or stopping point, often implying a clean cut in a sequence or process. Common phrases include 切りがない (endless) or 切りのいいところ (a good place to stop). It is derived from the verb 切る (to cut).
That is how Fuguro works. It brings 切り back for review right before you forget it, each time a little later, until it sticks for good. You hear it spoken aloud, and you meet it again in stories you can already read. The first five levels are free.