So in a double bond in ethylene, each Carbon atom contributes 2 valence electrons to fill the outer shell of each atom. Now the electrons are paired (this is just rote learnt) and they move around in orbitals around both atoms. At any point in time, the electrons could be near C1 atom, near C2 or randomly orbitting anywhere in between. But rather than just sharing 1 pair of electrons, they are sharing 2, so at any point in time, there is going to be more electrons located inbetween the carbon atoms than anywhere else in the molecule, and hence there is a higher electron density. This is naturally more reactive, because the electrons already have a higher electrostatic repulsion, it requires less energy to get them to break and react with other substances.
