You still haven't been too helpful in giving me a place a start... so again, I recommend reading the Wikipedia article, and doing a google search. That being said, let me say a few general things.
If you have a molecule---lets say NO2 (the example in the wikipedia article)---which has two (or more) possible configurations, it will often be in a combination between the possible states. In the figure, NO2 can have a double bond with either the left oxygen, or the right oxygen. In nature, NO2 will actual have kind of a 1 and a half bond on each side---more accurately, it will have partial double bond character. It other words it will 'resonate' between single and double bonds on each side.
Thus, the electron dot depictions aren't very accurate. Resonance structures are a way of trying to better describe the actual situation.
The reason molecules 'resonate,' is becomes it makes them more stable. The NO2 molecule is more stable with the double bond electrons shared between both sides of the molecule, than it would be if they were attached to only one side.
Let me know if there is something in particular I (or the forums in general) can try to elaborate on, or explain better. Please try to be precise.