============Short answer===================
If you are familiar and understand Newton's second law:
$$F = m\cdot a = m\cdot \dot{v}$$
Then you should know that one way to interpret it, is that:
the acceleration $a$ of a body with mass $m$ is proportional to the sum of forces acting on the body.
Similarly, keeping in mind that it can be proven that $\dot{H} = M$, the equation you describe can be written is a similar fashion:
$$ M = I_G \cdot \alpha= I_G \cdot \dot{\omega}$$
Where:
- $M$ is the resultant moments acting on the body
- $I_G$ the moment of inertia
- $H$ the angular momentum
- $\omega$ the angular velocity [rad/s]
- $\alpha$ the angular acceleration $[rad/s^2]$
Essentially, what this equation says is that :
the angular acceleration $\alpha$ of a body with moment of inertia $I_G$ is proportional to the sum of moments acting on the body.
Observe that there is a direct correspondence between:
- forces F and moments M
- mass $m$ and mass moment of inertia $I_G$
- acceleration $a$ and angular acceleration $\alpha$
===================Long Answer==========================
I won't bother with the long answer, because it would be impossible to give the generic case (see rotating systems of reference) within the space of this answer.
You might want to read Dynamics textbooks (Meriam and Kraige , Beer etc)