I have kept two charged plates(one positive and one negative) in contact with one another.So excess electrons will flow from negative plate to positive plate.But then why the wire joining the plates should also have free electrons?Aren't the electrons of the plates moving>?
Consider an analogy
Consider two water tanks with first tank having a higher water level in it. These tanks are connected to each other as shown in figure.
Case 1: The interconnect is a water filled hollow pipe: The water will flow from left tank to right tank.
Case 2: The interconnect is a hollow pipe filled with ice: There won't be any water flow.
In both cases, the pipes are filled with same molecules (\$H_2O\$). But the flow will happen only if the molecules are free to flow. Bounded molecules (as in ice), won't contribute to flow.
Electrons are like these water molecules. They will contribute to flow (current) only if they are mobile. So the excess electrons from negative plate to the positive plate will flow only if the interconnect have free (mobile) electrons in it.
The following information is extracted from All About Circuits:
A thin, solid line (as shown above) is the conventional symbol for a continuous piece of wire. Since the wire is made of a conductive material, such as copper, its constituent atoms have many free electrons which can easily move through the wire. However, there will never be a continuous or uniform flow of electrons within this wire unless they have a place to come from and a place to go. Let's add a hypothetical electron "Source" and "Destination:"
Now, with the Electron Source pushing new electrons into the wire on the left-hand side, electron flow through the wire can occur (as indicated by the arrows pointing from left to right).
In a nutshell, a conductive wire will have the presence of free electrons.
If a 'source' and 'destination' (in your case the negatively and positively charged plates) were introduced, then the electrons (including the free electrons) would be flowing through the wire and into the 'destination' plate (the positively charged plate).