It's difficult to find a map that gives a good visualization of the troop movements and intended goals of the Turks. This is the best one I've seen so far.

As best I've seen it described, the Turks are attempting to create a "safe zone" (for them) creating a barrier region 20 miles beyond their border, into Syria. If the Turks go further south, their only possible objective is ethnic cleansing of Kurds. And it does seem like they're preparing to do that.