You can draw a set (two or more) of resonance contributors using Lewis Structures for molecules and charged particles (ionic grouping of covalently bonded atoms) when there are pi electrons (or lone pair electrons such as those on a carbanion, C-) and there is a "sink" for them. A sink might be a carbonyl group (C=O), an electron deficient carbon atom (a carbonium ion, C+), and other examples. The pi electrons or lone pair electrons must be on an atom adjacent to the electron sink. There cannot be any sp3-hybridized atoms preventing the loosely held electrons from reaching the sink. The spatial position of all atoms are held constant. The charge on the molecule is spread over the atoms of the contributors, not localized or stuck on one atom. Remember that not all resonance contributors are significant; the "best" resonance contributors are those that have the same number of single and double bonds, no separation of charges are created (no new + or - charges on atoms), and if a formal charge must be included, the most important contributor has negative charges on the most electronegative atoms, and positive charges on the most electropositive atoms.
Above all-all significant contributors MUST obey the octet rule-with the exception of 3rd row elements which may have an "expanded octet" and accept 10, or even 12 electrons (e.g. Si, P, S).
Resonance contributors are a concept (thanks again, Linus Pauling!) that helps to understand the stability or instability of a molecule. They help predict the region where a chemical species is most likely to be attacked by a nucleophile, or why they are resistant to attack. In short, they help us when attempting to make sense of the mechanism, or pathway a reaction might take.
Resonance is not merely a concept; the resonance energy of a molecule can actually be calculated and verified by experiment. It is essential to remember that the actual structure of a molecule is a hybrid of all of the resonance contributors combined. They are not interconverting or oscillating from one to another like a chemical reaction. Resonance increases stability by increasing the bonding between adjacent (more covalent bonds) atoms and by distributing charge over a greater number of atoms (delocalization).
ANSWER TO QUESTION: The easiest way to understand resonance is to get a piece of paper and a pencil and start drawing them. Read and re-read the portion of your textbook that explains resonance. But reading alone will not "sink" the concept into your consciousness; taking pencil in hand and putting pencil to paper signals to your brain that there is something important going on.
There are rules that must be adhered to in order to make use of the concept successfully. I won't repeat the rules here; they are in every organic chemistry book. A handbook that my students have found useful for understanding resonance theory is called "Pushing Electrons: A Guide for Students of Organic Chemistry" by Daniel Weeks (ISBN # 978-0030206931)-you can buy an older edition online for under $1. For free, you can download ACD Freeware, which is a program for drawing molecules (and so much more) at acdlabs.com