The extent is the area something covers. That could be physical space or something like being prosecuted to the full extent of the law.
Use the word extent when you are discussing how far something extends — how far it reaches. If you're an expert, the extent of your knowledge is wide. If you own a lot of property, the extent of your land is huge. The full extent of something is like the limit — that's the end of it. If you've reached the extent of your patience, you're out of patience. If an earthquake destroyed your house, the extent of the damage was severe.