An inertia system of coordinates is a coordinate system that we can approximate to be stationary.
For instance, we can describe the displacement of a baseball (the object of interest) relative to the baseball field (an inertia system of the baseball). Since both the baseball and the field are subject to the same rotational motion of Earth, the movement of the baseball can be described relative to the seemingly stationary field.*
Einstein gives us a way to determine if a system of coordinates is an inertia system:
A system of coordinates moving in the same direction and at the same rate as a system of inertia is itself a system of inertia.
*For the purposes of this example, we have ignored the (negligible) effect of Earth's rotation. An observer on the surface of Earth must be accelerating to follow a circular path, and the entire system is subject to the non-inertial effects of gravity.