Effectively each atom now has a share of both the electrons. The electron density between the two nuclei exerts an attractive force on each nucleus keeping them held tightly together in a covalent bond. A covalent bond forming between two hydrogen atoms. It is also possible for two atoms share more than one pair of electrons, sharing two pairs results in a double bond and sharing three pairs results in a triple bond. Electronegativity is a measure of how powerful a atom is in a molecule to attract electrons.
Polarization is a term given to name the unequal sharing of electrons in a covalent bond.
Molecules that have unequal sharing of electrons are called polar molecules and dipole molecules are ones which have the charge separated, therefore all polar molecules must have a dipole attraction. Non-polar molecules are ones in which there shapes are symmetrical so the electrons are evenly distributed. Polar molecules have a permanent dipole in other words they have a permanent separation of charge. As a result of this, polar molecules are attracted to one another by forces called permanent dipole-permanent dipole interactions, in which the negative end of one molecule is attracted towards the positive end of another. These interactions decrease quite rapidly as the distance between molecules increases.