What actually is impulse? In my textbook it is mentioned that “impulse is used to get an idea of about the change in dynamical state of a moving particle”,but what does impulse actually mean?
 A: Both @Farcher and @Dale are correct as the full answer is the combination of their answers.
You can think of impulse as the currency of momentum if you want to make a money analogy. Momentum is how much money you have in your bank account, and impulse is the amount of money you deposit or withdraw.
Impulse has two descriptions

*

*Physically an impulse is a way to describe a change in momentum, like with the analogy above.
$$ \Delta p = p_f - p_i = j \tag{1}$$
where $\Delta p = p_f - p_i$ is a change in momentum $p$, and $j$ is an impulse.


*Mathematically it is the area under a force vs. time curve $$j=\int F\,{\rm d}t \tag{2}$$ if force is an applied force, and not restricted to short time periods, just as rocket engines have impulse values, and they burn over several seconds. Hence why the units of momentum are often stated as Newton-second $\text{[N s]}$.
But this begs the question, of what is momentum. I know mathematically you know momentum is $p=m v$, what does this mean physically?
The answer comes from (1), as I describe momentum as the quantity of impulse needed to completely stop a moving object. So I understand momentum, in terms of impulses and not the other way around.
Suppose you have a body with momentum $p_i \neq 0 $ and you  want to find the impulse $j$ needed to completely stop the body and make $p_f = 0$
$$\Delta p = p_f -p_i = -p_i = j$$ $$ |p_i| = |j|$$ and this makes momentum measurable, because impulse is measurable.
Conservation of momentum is automatically enforced in this system, just as as with banks the total amount of money is conserved when you pay for something (what leaves your account goes into another account). An impulse leaving a body (and reducing its momentum) goes into another body (and increases its momentum) in a way that total momentum is conserved, and all as a consequence of Newton's 3rd law (equal and opposite impulse as a result of equal and opposite forces).
$$\require{cancel}  \begin{array}{r|cc|c}
\text{momentum} & \text{body 1} & \text{body 2} & \text{total} \\
\hline
\text{before} & p_{1} & p_{2} & p_{1} + p_{2} \\
\text{after} & p_{1}-j & p_{2}+j & p_{1} \cancel{ -j }+ p_{2}  \cancel{+j} = p_{1} + p_{2} \end{array}$$
Furthermore, the above can be extended into vector notation, where not only the magnitude and direction of momentum is defined, but also the point in space where momentum is defined. This leads to the law of conservation of angular momentum.
A: An impulse is a change in momentum, usually with the connotation that it is very brief or sudden.
A: In the context of Mechanics it is $J = \int F(t)\,dt$, ie the area under a force, $F$, against time, $t$, graph and has the unit $\rm N\,s$.
Often it is taken to mean a force which acts over a very short period of time compared with other time scales relating to the system.
For example, when two billiard balls collide and the time of collision (when the balls are in contact) the forces acting on the billiard balls can be termed impulsive because they act over a much shorter period of time than the time taken for the balls moving from their original positions..
Thus in terms of the complete motion of the billiard balls the collision can be though of as occurring instantaneously.
The from Newton's second law, force is equal to the rate of change of linear momentum, $F=\frac{dp}{dt} \Rightarrow \int F\,dt = \int dp$, the impulse is equal to the change in momentum.
A: Impulse is the momentum gained or lost by applying a given force for a given amount of time.
A: In classical physics, the formal definition of the impulse is the integral of the force, 'F' over a certain time period t.
Mathematically, it looks like this:  ${\displaystyle \mathbf {J} =\int _{t_{1}}^{t_{2}}\mathbf {F} \,\mathrm {d} t}$.
A: Newtons seconds law for a body is a law of motion which applies for all time instances. If we are to accumulate the information of all the forces over a period of time, we would have to integrate this law.
We have $ma= F$. The integral of LHS with time is just change in momentum and right we name as impulse.
