Inertia
Inertia is the tendency of an object to resist any change in its motion, staying at rest or moving at constant velocity.
Definition
Inertia is an object's resistance to changing its motion: things that are still want to stay still, and things that are moving want to keep moving. More precisely, it is the tendency of an object to resist changes in its state of motion, whether that state is rest or constant velocity, and the amount of inertia depends only on mass, so Newton's first law is often called the law of inertia. Quantitatively, inertia is measured by inertial mass, the constant $m$ in $\vec{F} = m\vec{a}$ that sets how much acceleration a given force produces. Experiments show inertial mass equals gravitational mass to extraordinary precision, an equivalence Einstein made a founding principle of general relativity. For rotation, the analogous quantity is the moment of inertia $I = \sum m_i r_i^2$, which depends on how mass is distributed about the axis.
Example
When a bus starts moving, you feel pushed backward into your seat because your body wanted to stay still while the bus started to move. Flicking a $2\ \text{kg}$ bowling ball and a $0.1\ \text{kg}$ tennis ball with the same $1\ \text{N}$ force gives the tennis ball $10\ \text{m/s}^2$ but the bowling ball only $0.5\ \text{m/s}^2$, because the bowling ball's greater inertia resists the change more. Scaling up, a $1{,}500\ \text{kg}$ car and a $15{,}000\ \text{kg}$ truck each receiving a $3{,}000\ \text{N}$ net force accelerate at $2\ \text{m/s}^2$ and $0.2\ \text{m/s}^2$ respectively; the ratio of accelerations is the inverse ratio of their inertial masses.
Key Insight
Inertia is not a force. It is a property that every object has just because it has mass, and it does not push or pull anything. It works in space too: an astronaut pushing a $500\ \text{kg}$ satellite finds it just as hard to get moving as on Earth, even though it is weightless, because inertia depends on mass, not weight. That fact lets you weigh things where gravity is useless. Astronauts on the space station measure body mass by oscillating on a spring device and timing the period, which depends on inertial mass alone.