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I can understand the operation of dividing two units for example: 1 m/s it means that the object covers the distance of 1m in one second but really I can not understand the operation of multiplication for example : Force = Kg . m/s^2 what does this mean?

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Momentum $p$ has the units $kg \frac{m}{s}$, which literally means "the momentum that an object of mass 1kg has when it is moving with 1 $\frac{m}{s}$".

In a similar fashion, force $F$ represents the change in momentum ($F = \frac{dp}{dt}$), that is "how much force is required to change the momentum by 1 $kg \frac{m}{s}$ per second", or alternatively from $F = m \cdot a$ "how much force is required to accelerate an object of mass 1kg by 1 $\frac{m}{s^2}$".

It works similarly for any other unit, too.

  • intensity ($\frac{W}{m^2}$): "how many Joules fall on an area of 1 $m^2$ per second?" (W = J/s)
  • angular momentum ($kg \frac{m^2}{s}$): "how much angular momentum does a 1kg object have that is rotating at a radius of 1m and moving at a tangential velocity of 1$\frac{m}{s}$?"
  • Boltzmann constant $k_B$ ($\frac{J}{K}$): "by how much does the energy of $N$ particles change, if temperature is changed by 1K?"
  • electric field ($\frac{N}{C}$ or $\frac{V}{m}$): "what force in $N$ would a charge of 1C feel in this electric field?" or "what potential difference in $V$ is there at points 1m apart in direction of the field?"

Since this is often cumbersome, however, there are derived units for common quantities: Newton (force), Joule (energy), Tesla (magnetic flux density), etc.

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  • $\begingroup$ +1 for the clear explanation $\endgroup$ – Abhinav Apr 25 '18 at 9:47
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The momentum (p) of an object is found by multiplying the objects mass (m) in kilograms (kg) by it’s velocity in metres per second (ms-1).

Momentum is a vector and it’s unit is the kilogram metre per second (kgms-1).

According to Newton's Second law

The rate of change of momentum of an object is directly proportional to the resultant force applied and is in the direction of the resultant force. The resultant force is equal to the rate of change of momentum.

F=$\Delta(mv)$/$\Delta t$

So from the above formulae ,you can see what the units mean in the expression.

Definition of newton

A newton is the force required to give a mass of 1 kilogram (1 kg) an acceleration of 1 meter per second per second (1 m/s2). It is abbreviated as N.

This unit of measurement is in the metric or SI system and is used in scientific work more than other units of force.

1 N is equivalent to 1 kg-m/s2.
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