Question

Basically What does Discrete and Continuous charge distribution means?

Answer 1

Discrete charge distribution means several charges, say q1 at one location, q2 at another location, etc. To determine the effect of all those charges, you add up their individual effects (vector addition).

A continuous charge distribution means charge smeared out along a line (wire), or over a surface (plate), or thru a volume of space, perhaps the same amount of charge per unit of distance, area, or volume. Or perhaps the amount of charge, per unit distance, area or volume, will vary according to some formula. To determine the effect of that smear of charges, you have to integrate instead of adding. For example, if the charge is smeared along a line, and the density is per unit length, then you would consider an infinitesimal bit of the line, say length dl (vector), and its charge might be lambda*dl if lambda is the charge density per unit length.

Answer 2

I should probably also mention that the examples of continuous charge distribution seen in introductory textbook problems assume that the wire or plate is non-conductive. If the wire or plate is conductive, the charge distribution will most likely not be uniform, as like charges repel.

Answer 3

Mostly correct, i believe, though in a roundabout, mathematical manner.
Put concisely, they are is exactly as they sound: continuous means that a charge is equally spread throughout an object, while a discrete one has more or less of an erratic charge density.
This is why (i believe) that it is a non-conductor that would more likely have a discrete charge. This is how static electricity is created. Their property of charge not freely flowing through them allows for a net concentration of, for example, electrons, to from (via friction). This property is rarely observed in conductors such as metals. Plastics (which are used for electrical insulation) are ideal for a practical example of static electricity.