The more stable is a compound, the more "chemical inertia" will it show. Think about the more reactive compounds you know - they will be very frequently charged, geometrically tensionated or unstabilized in any other way. Definitely stability and reactivity are not good friends.

The resonance stability is more specifical. When talking about benzenoid compounds, the specifical geometrical is very important. For example, if there is a charge, the more different positions can it take in different resonating forms, the more stable will the compound be; if a negative charge can be "resonated" to a electronegative atom (like O or N), it will help stabilizing the compound; the more different conjugated forms of the molecula you can draw using resonance, more stable will it be, and so on.
Keep in mind that the molecula is not "jumping" to one resonating form to another, but it is kind of "in the middle" of them. So, if a charge can be "resonated" to three different atoms, its not that there is a charge in one of them at a time, constantly changing position, but that there is a piece of the charge in each of themm all the time, which is a comparatively more stable situation.