Definition
Inertia is the tendency of an object to keep doing what it's already doing: a moving object keeps moving, and a resting object keeps resting. If no outside force acts on it, every object stubbornly holds on to its current state of motion.
What happens when a bus brakes hard
Say you're riding a bus and the driver suddenly hits the brakes. Your body lurches forward. Now flip it: a stopped bus suddenly pulls away, and your body snaps backward. You're not pushing yourself on purpose, yet it happens automatically.
The reason is simple. Your body was traveling forward with the bus, so it wants to keep moving forward even after the bus stops. Your feet touch the floor, so they stop with the bus. But your upper body wants to keep going, so it tips forward.
This is also why we wear seat belts. When a car hits a wall and stops, the people inside still want to keep moving at the car's original speed. The seat belt acts as an outside force and holds your body back.
The heavier it is, the more stubborn it gets
You can stop a rolling soccer ball with your foot. But you can't stop a huge truck rolling at the same speed with your hands. The more mass an object has, the more strongly it resists any change in its motion.
In physics, mass isn't just "the amount of stuff." It's also described as a measure of how much inertia an object has. An empty stroller is easy to push and easy to stop. A cart loaded with heavy cargo takes a lot of force to get moving, and a lot of force to stop.
The same idea works inside a spaceship where nothing feels heavy. A giant floating boulder will move if you nudge it, but it speeds up very slowly. To get it moving fast, you have to push hard for a long time. And once it's moving, it keeps going at that speed unless something stops it. By the way, you feel weightless in a spaceship not because there's no gravity, but because the ship and the people inside are falling together.
A more precise way to put it
In everyday life, a ball you roll across the floor seems to stop on its own after a while. So people long ago wrongly assumed that "objects naturally want to stop, and you have to keep pushing to keep them moving."
But the ball doesn't stop because inertia disappears. It stops because outside forces, namely friction from the floor and air resistance, keep working against it. If there were no friction, no air resistance, and no other forces like gravity pulling on it, a ball you threw would fly in a straight line at the same speed forever.
So inertia isn't a "force" that makes things move. It's an object's "built-in property" of keeping its state when nothing interferes. Galileo and Newton worked this out, and Newton wrote it down as his First Law of Motion.
Common misconceptions
Inertia is a force that pushes an object to keep moving forward.
Inertia isn't a force. It's a property of objects. Nothing is pushing from behind to keep the object going. There's just nothing stopping it, so it keeps its original state of motion.
Where you meet it
When a hammer head gets loose, you can bang the bottom of the handle on the ground. The head keeps moving down because of inertia, and it wedges tightly onto the handle.
When you beat a dusty blanket with a stick, the blanket gets pushed away but the dust tries to stay where it was, so it shakes loose from the blanket.
Pull a roll of toilet paper slowly and it unrolls. Yank it fast and the roll's inertia keeps it in place, so the paper tears off cleanly.
In one sentence
Every object has a built-in property called inertia: unless an outside force acts on it, it keeps its current state of motion forever.