Resonance is a situation where there are two structures or more that we can draw - (in the case of SO2 one with the double bond on one of the oxygens and the other structure with the double bond on the other oxygen).
The concept of resonance says that as both structures are equally likely then the actual structure will involve and average of both (or all) of them.
We say that the structure 'resonates' (vibrates in harmony) between one structure and the others so fast that they are all contributing equally to the true structure.
Resonance has the effect of adding stability to a molecule or ion as the electrons are effectively more spread out over the structure and consequnently the charge density of the electrons cannot be so concentrated in one place.
It is this concentration of charge density that gives rise to reactivity in covalent molecules (among other factors)