Polar Bonds and Electronegativity 
When two identical atoms form a covalent bond they have equal pull on the covalent electron pair.  The electrons used for bonding are therefore shared equally  and no one atom has more of the electron pair than the other.    However when a molecule like HCl forms, the chlorine atom has a much stronger attraction for the single covalent bond  and the electron pair ends up spending most of its time closer to the chlorine atom than it does the hydrogen atom.   Since the negative charges of the electrons spend most of their time in the vicinity of the chlorine, the chlorine atom takes on a partial negative charge. This charge is more than what the neutral chlorine atom had but not as strong as the charge acquired by a chloride ion that takes the electron and keeps it.  The negative charge gained by the chlorine atom is balanced out by a partial positive charge gained by the hydrogen as the hydrogen's electron is pulled out of place.

The charges on each atom are less than the full +1 and -1 found in ions. For this reason they are called partial charges.   A bond that carries partial positive and negative charges on opposite ends is called a polar bond, or a polar covalent bond.  The term polar comes from the idea that the opposite charges are at opposite poles of the bond.  Because there are two poles of charge involved, the bond is said to be a dipole.

The polar bond in HCl causes the molecule to act as if the entire molecule had opposite charges on it. For this reason the HCl is a polar molecule.  The extent of the polarity in the dipole can be caluclated very simply.

Pauling's Table of Electronegativities
H
2.1

Li       Be                                                                                            B     C     N    O    F
1.0     1.5                                                                                          2.0  2.5   3.1   3.5  4.1

Na      Mg                                                                                        Al    Si      P     S     Cl
1.0      1.3                                                                                        1.5   1.8   2.1   2.4  2.9

K      Ca     Sc     Ti      V     Cr     Mn   Fe     Co   Ni    Cu    Zn     Ga    Ge    As    Se   Br
0.9    1.1    1.2    1.3    1.5   1.6    1.6   1.7    1.7   1.8   1.8   1.7     1.8    2.0   2.2  2.5   2.8

Rb       Sr    Y      Zr     Nb   Mo    Tc   Ru     Rh    Pd   Ag    Cd     In     Sn    Sb    Te    I
0.9      1.0   1.1   1.2    1.3   1.3    1.4  1.4     1.5   1.4   1.4   1.5     1.5   1.7   1.8   2.0   2.2

Cs       Ba    La    Hf     Ta    W     Re   Os      Ir     Pt    Au    Hg     Tl     Pb    Bi    Po    At
0.9      0.9   1.1   1.2    1.4    1.4   1.5  1.5     1.6   1.5   1.4   1.5     1.5  1.6    1.7  1.8   2.0

Fr        Ra    Ac
0.9       0.9   1.0
 

Just how polar a a polar bond is can be calculated using a Table of Electronegativities.
Electronegativity is defined as the amount of attraction a nucleus has for an electron.  Metals have low electronegativities because the shed electrons readily.  Electronegativities are high in atoms that like to gain electrons in order to fill out their shells.  The trends in the periodic table are that electronegativities increase as you go up a group and from left to right across a row.  Take any two electronegativites and find their difference.  The one with the high electronegativity will be negative compared to the other.  If the difference is greater than 1.7 then the bond formed will be ionic. If the difference is zero then the bond will be non-polar covalent.  Any bond formed with a difference between 0.1 and 1.6 is considered polar covalent.  A polar covalent bond with a difference is 1.6 would be very polar compared to one with a difference of 0.