Bonding
Covalent bonds exist between atoms when those atoms are sharing some of their outer (valence) electrons. These atoms share these electrons in order to reach a more stable form by filling their outer (valence) electron shell. Basically, every atom (with the exception of hydrogen and helium, which have 2) have 8 spots in their outer orbital (electron shell) that they'd like to have filled. So atoms will share, steal, or give electrons in order to fill that outer shell. Covalent bonds are represented by lines connecting the atomic symbols of the elements in a Lewis dot structure (see below).
Depending on how many pairs of electrons are shared between the atoms, there are different kinds of covalent bonds. If a single pair of electrons is shared, it is a single covalent bond. If two pairs of electrons are shared, it is a double covalent bond. And finally, if three pairs of electrons are shared, it is a triple covalent bond.
Ionic bonds occur when atoms are a little more selfish...or more selfless. Instead of sharing, atoms that form an ionic bond either steal or give away electrons from or to one another. This means that one atom lost an electron and one gained an extra electron. If an atom lost an electron (remember, electrons have negative charges), that is like losing a negative. If you subtract (or lose) a negative, you become positive. So the atom that lost an electron is now a positive particle, known as a positive ion (cation).
The atom that gained an electron took on an extra negative particle. So, if it was neutral before this bond formed, it is now negative. So it is a negative ion (anion). Remember, an ion is a charged particle.
So why would some of these bonds involve stealing of electrons? Why can't we all just share? Well, if you remember from basic chemistry, some atoms are more electronegative than others. This means that they are more attracted to electrons than others - in other words, they are greedier with their electrons. For this section, I will be stating that atoms 'want' electrons. This is just an easier way to imagine this phenomenon - obviously atoms don't actually want anything.
If an atom is greedy enough (compared to the other bonding atom), then the first atom may steal the electron away. This would be like the ionic bond above. Chlorine REALLY wanted that electron. Sodium didn't really care too much because it would be happy to get rid of the electron (then its outer shell would be full - exactly what it wants).
So what if atoms want the electron equally? Well, in that case, they are going to share the electron pair right in the middle. This is commonly seen with carbon and hydrogen. They both want the electron a similar amount, so the electron will stay in the middle of them most of the time. This would be considered a nonpolar covalent bond. It is covalent because the electron is shared, not given away/stolen. It is nonpolar because the electrons stay in the middle most of the time. They're both playing tug-of-war for that electron pair, but they are equally strong.
But what if one atom REALLY wants that electron pair, and the other is just kind of lukewarm about it? Well, let's look at an example. In the case of water, there are 2 hydrogen atoms, each bonded to an oxygen. Oxygen LOVES electrons, so it's going to be putting its all into that tug-of-war. Hydrogen doesn't put up much of a fight. As a result, the electrons are going to spend more time near the oxygen atom.
What happens if somebody really negative spends a lot of time around you? You probably get a little negative too. Not as negative as they are, but at least a little more cynical. Oxygen, in this example, does the same thing. The electrons spend more time with oxygen, so oxygen has a partial negative charge. It's not an ion, so it's not an ionic bond. It is just slightly negative. If the electrons are spending more time with oxygen, they are spending less time with hydrogen. So, the hydrogens will have a slightly positive charge. This is known as a polar covalent bond.
These partial charges in polar covalent bonds are typically represented with the symbols shown here.