And what makes a resonance structure more 'stable'? Charges, bonds, anything else?
It's because the formal representation of the molecule is not the reality. Molecules where multiple resonance structures can be drawn out are actually a hybrid of all these resonance states. For example, benzene does not actually alternate its double bonds, but instead has a 'delocalised' zone where the electrons are free to roam throughout the ring (which explains the alternative representation of benzene with the circle in the ring, rather than the Lewis convention of drawing 3 conjugated double bonds).
Now, the reason why this is more stable is because the electrons in the molecule are more delocalised, and less confined in the same packet of space. This helps to lower the energy of the electrons (lets it find a more even 'equilibrium'), hence stabilising the molecule. To help improve your conceptualisation: does it make sense for a high energy electron (whizzing around) to stay in one tiny packet of space, or does it seem 'better off' when given more room to move around? It should make intuitive sense that the more delocalised an electron is, the more likely that state is (and hence more stable).
I'm not sure if this was what you were asking though. Did you mean to ask what features help a particular resonance state contribute more stability to the overall structure? Usually it involves keeping like charges away from each other - have you studied electrophiles and nucleophiles yet? There are some groups that prefer electrons more than others for example, or prefer positive charge more than others (due to electronegativity). Resonance states which place the charge nearer to the group that prefers it are particularly stable, and contribute markedly to the stability of the overall molecule.
If there are any more questions, feel free to ask. I almost forgot why this was the case, thanks for reviving my memory.