Question: First off, what is meant by the potential of the conductors? Also potential difference between the two conductors is a function of distance from either right? Then why does it have an exact value. For example take two conductors having equal and opposite charges and separated by a small distance. Now according to my book, any point between them has the same potential. But, when the point is closer to positive plate, should it not have more affinity towards one than other, there shouldn't also be a point where the potential is zero?? Sorry if this is a dumb question but I really don't get the topic.

Answer: 
The electric potential of a point in space is defined by the mechanical energy that it takes to get a (positive) unit charge to that point. We usually define the potential of an infinitely distant point as zero, and then the movement of our test charge is from infinity to the point for which we want to measure the potential. 

In case of a capacitor the conductivity of the plates guarantees that the potential is the same on every point of the surface of the two conductors because there is no electric field component parallel to the surface of a conductor. Since there is no field component parallel to the surface, there is no force on a test charge parallel to the surface, either, which means there is no work to be performed as long as we are moving parallel to the surface. 

This means that one can assign a potential to each conductor without talking about the physical coordinates any longer.
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> First off, what is meant by the potential of the conductors? 
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The "absolute" potential is of no importance in a working capacitor. In fact, it's practically impossible to determine. The potential difference between the plates (or between a plate and some ground/earth plane) is the important factor in the capacitance relationship, $C=qV$.

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> Now according to my book, any point between them has the same potential. 
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Your book (if you have quoted it correctly) is wrong. The **electric field** magnitude can be considered constant for plate separations which are small compared to the plate size. The potential difference is then $Ed$, where $d$ is the distance from the plate.