To understand rotational inertia, we had better explain inertia in general. The more inertia an object has, the less it responds to being pushed. The more mass in an object, the less it responds to being pushed. A light push sends a ping-pong ball flying, while a light push on a bowling ball has almost no noticeable effect.
Rotational inertia is a resistance to change of rotation.
The more rotational inertia an object has, the less it responds to being spun. The outside parts of a spinning object have to move much faster than inside parts near the axis. How an object is built, and along what direction you want to spin it, also affect the rotational inertia. Argonne National Laboratory, Division of Educational Programs, Harold Myron, Ph.D., Division Director.