Although to make a covalent bond, the two atoms in the bond must be similar enough in strength that neither can take an electron from the other, that does not mean that their strengths are the same. If the two atoms have different strengths, then the electrons may be unequally distributed. In other words, if one nucleus pulls harder on the electrons than the other does, the electron cloud may be warped toward that atoms, like this:
When this occurs the end that has more electron density has a partial negative charge (the atom on the left is holding onto its own electrons strongly and has “claimed” more than it's share of the other atom's electron) while the other end of the bond is partially positive (the atom has lost a share of it's electron and has gained very little if any of the other atom's electron to balance this loss). This uneven distribution of electrons in a bond resulting in partially charged bond ends is called polarity and a bond that exhibits polarity is called a polar covalent bond, or just a polar bond.
One way to show the partial charges on such a bond (in this case, the bond betwee chlorine and hydrogen) is shown below. The symbol is a lower case delta (Greek d) and means partial.
A note about polarity in bonds:
Although any bond in which the two atoms do not have identical electro-negativities is, in essence, polar, our ability to measure that polarity is limited. As a result, we consider any bond in which the electronegativity difference is less than 0.3 to be a non-polar bond.
Because drawing the warped electron cloud is more work than people generally want to do each and every time they need to represent polarity, a symbolic shortcut was invented. Let us use the example of a bond between hydrogen and chlorine. This bond is polar toward the chlorine, since it is more electronegative.
We represent this polarity by drawing an arrow above the bond which points toward the chlorine (showing the direction the electrons move). The other end of the arrow is turned into a plus sign to indicate the positive end of the bond.
Polarity is important because, as we know, positive things attract negative things. This means that a polar bond can attract another polar bond. This attraction will not be a strong as the attraction between ions (since the charges are not complete) but it is strong enough to have major consequences throughout chemistry and biology.