Inertia is simply Newton's first law of motion. An object at rest will tend to stay at rest unless an outside force acts on it, and an object in motion will tend to stay in motion unless an outside force acts on it.
Newton's 1st law of motion can be observed when a car goes around a turn at a high rate of speed. It feels like the occupants are being thrown to the outside of the turn, but they're not. The car and occupants are in motion in the same direction. When the car turns, the occupants want to stay in motion in the direction they were originally going (i.e. they have inertia). The side of the car, and their seat belts, make them change direction with the car, and the inertia is what "throws" them to the outside of the turn.