Imagine you're on a merry-go round. You could calculate physics as if you and the merry-go-round were rotating, and that will be fine. Alternatively, you could pretend you're not rotating (choosing a non-inertial reference frame). However, if you want physics to still work, you have to introduce centrifugal and coriolis forces to make everything work out properly (this is the force you feel "pushing" you out to the edge).

Now in general relativity, inertial reference frames are those that are in free fall. An example of an inertial reference frame would be an orbiting satellite. Note that there is no gravity in an inertial reference frame like a satellite. Now, you can pretend that standing on the surface of the earth is an inertial reference frame (ignoring totally the rotation for now), but to make everything work out properly, you need to introduce a new force accelerating you downward: gravity.