What is the "displacement" of the object in the definition of work? Work in physics is mathematically defined as force $F$ applied on an object multiplied by the displacement $d$ it covers in the direction of the force. In a system where, a restrictive force exists like friction due to contact between objects or in a field where work done changes into potential energy, displacement is finite.But according to Newtons second law of motion when a force is applied on an object, it produces acceleration in that object which causes a change in velocity in a "certain" time. Moreover when the force has been applied, according to Newtons 1st law of motion it should displace "infinitely" with a constant velocity which is changed due to the force applied. My question here is that what is the real definition of 'displacement' in work formula?
$$ W = F d \cosθ$$
Is the displacement infinite making work infinitely increasing or it is the displacement covered by that object while the force is being applied or when there is acceleration being produced?
 A: The work occurs while the force is applied.
So the d in the formula is the distance the object moves while the work occurs.
Independent of that, the object, which was accelerated by the work, wil displace further afterwards.
There are two uses of the term "displacement" for different things in your question I think. Sorting that out may help clear up your confusion about it.
The "certain" time is the time during which work is done, because force is applied. After that, the object will move with it's new velocity, caused by the acceleration by the work. It will keep that velocity until a new force is applied, changing it's velocity again. 
That new force could be friction, stopping a piece of wood pushed by the force, or gravitational attraction of a planet nearby an asteroid. 
A: 
Work in physics is mathematically defined as force F applied on an object multiplied by the displacement d it covers in the direction of the force.

Not really. The original definition, from the early 1800s, was applied to the amount of force needed to lift a bucket of water. Since this was occuring in gravity, the need for the term "during the application of the force" was not needed, that was assumed in the experimental setup - the bucket stopped when you stopped applying the force.
So then the definition isn't automatically useful when considering cases outside gravity, which is what is causing your confusion (and everyone else's, this is one of the most commonly asked questions here). So then you add the proviso that was inherent but unspoken in the original definition, "during the application of the force". You can see this in the Wiki article you linked to.
My suggestion: whenever you get confused by work, apply the work-energy equivalence. So if someone defines work as the change in energy and the result seems odd, reformulate the question as work being the force over distance. And if, as in this case, the force over distance seems to be odd, then consider it as a change in energy.
So in this case it seems odd that work isn't infinite when the displacement goes on forever. Ok, reformulate the same question in terms of energy. Was infinite energy applied to the object? No? The mystery instantly disappears.
A: To give a short formula based answer, solving for $S$ from the equation:   $v^2 = u^2 + 2as$  and substituting it into the equation:   $W = fs$   gives      $W = \Delta KE$. Which is true based on the work energy theorem.  Consider that we used an equation that defines $S$ in a context of constant acceleration. So, we used the displacement that is covered during acceleration, not constant speed. Therefore, the $S$ in the definition of work is displacement during the period of application of force, which is the period of acceleration where the kinetics energy changes because of change in velocity. This brings the harmony between the basic definition of work done  and the work energy theorem. In other words, the work energy theorem tells us exactly which displacement is there in the definition of work done. But we need some further explanation on what happens when there is resistive force like gravity or friction.
