Both non-polar and polar bonds are covalent and made up of pairs of shared electrons. The electrons are attracted by the nuclei and the atoms are held strongly together. Covalent bonds are very strong.
The difference is the way that the electrons are shared and this refers to how the electrons spend their time in the region of space between the nuclei. In the pure (non-polar) bond, the electrons are shared equally though are sometimes nearer one atom than the other. However it is a 50:50 share. The two atoms have equal abilty to attract electrons so have similar or small difference in electronegativity eg. O2, Cl2, H2, PH3. As the molecule are not polar the attraction between these molecules is low, so MPt and BPt are relatively low. (London forces)
With the polar bond the shared electrons spend more of their time closer to one atom than the other because one of the atoms has a greater attraction for bonding electrons (known as electronegativity). The result of this is the atom which has >50% share of electron becomes slightly negatively charged (delta -) while the other atom, with <50% share of the bonding electron becomes delta+ eg in HCl gas, Cl has higher EN than H so Cl has the greater share of the two bonding electrons. So the molecule is delta+ H-Cl delta -. Remember each H atom has 1 proton and 1 electron, while the Cl atom has 17 protons and 17 electrons. If the hydrogen atom's only electron spends more of its time closer Cl, the Cl atom will have a slight negative charge while H atom will have a slight positive charge.
The molecule is polar (has permanent charges (dipoles)). The important consequence of this it that one molecule is attracted to another molecule. eg H-Cl...H-Cl etc. This tends to affect properties such as MPt and BPt and cause higher than expected values. Sometime the attraction between molecules is called the hydrogen bond as in water and HCl. The polar nature of water is the reason why so many ionic compounds are pulled apart by water molecules when they dissolve.