Metals are in solid state. So conductors are basically solids. (Don't take it too much. There are no solids in quantum physics). A conductor is hence characterized by tightly packed atoms with plenty of availability of valence electrons that are ready to get off from what that holds them. Also a good conductor like silver, iron etc. have very good atomic radius which makes their valence electrons very less bounded to the nucleus. Hence they have a high chance to get out from the atom if you give a little bit energy. Once they gain it, they will get out of the atoms and are no more a part of it. Then they are called free electrons.
Now these electrons determine the conduction in the metal. But, who determines the conductivity? Of course, our free electrons are free to move. But are they?. The atoms are tightly packed. So the electron has a higher probability of collision with the atoms or ions in the lattice. Once you connect the conductor to a power source, then the electrons get accelerated by that field. These electrons, but however, move only with an average velocity as the accelerated electrons lose some of their kinetic energy by collision with atoms. But the effect of electricity moves very fast as an accelerated electron radiates electromagnetic energy which gets carried by other electrons. This is why the bulb glows at the same instant when you switch on the bulb.
Now, about resistance. For certain metals (resistors are also metals) the inter atomic spaces are so small and the electron loses majority of it's energy due to inelastic collisions with the massive atoms. This means there goes some energy of our electron. This lost energy appears as the lattice heat. A resistor is characterized by such huge energy lose. Also the thermal vibration of atoms will be much more which increases the power dissipation. You should note that the conductivity of a conductor decreases with increase in temperature. So the resistivity is the characteristic property of a metal.
if electrical resistance a element is zero can we conclude that it should has not any vibratios?
No, the superconductors, for example can be considered as zero resistance conductors. But there are still lattice vibrations. See the BCS theory of superconductors. But at absolute zero, there is no entropy and there will be a perfect ordered state. But at absolute zero, the microscopic particles have some energy. So we cannot say, they are not moving even at absolute zero of temperature, which is practically not possible. A superconductor, as you increase the temperature, behaves like a normal conductor. So, it is not possible to have zero vibrations of atoms/ dipoles. There will be always vibration.