What is the difference between ownership and easement?

Our driveway goes through our front neighbor's side yard.
The builder's plot labeled the driveway as 12'x200' easement.
The county counted the area as part of our lot. We are
paying tax, mowing on the drive sides.

We also also have 30'x100' public sewage easement that runs
through our backyard (60' away from our house), from the county.
We are paying tax on that area.

If someone hurts himself in the easement, who's insurance
will pay for it?