Resistance

Increased resistance to elemental damage (Fire, Ice, Divine, Shadow, Poison) will result an increased chance that the elemental attack will do no damage.

This can be shown visually when the Show Damage option has been activated and a "Resist" appears in lieu of a damage number.

It has been mentioned in the official forums by Stephen that:

Ideal resistance is equal to (13 * level). That is, if you have 13 resistance at level 1 then you'll resist damage about 75% of the time. At level 100, you'll need 1300 resist to have the same percentage.

In PvP, the basis for resistance is lower. Instead of 75%, I believe the resistance basis is 35%.

(Link to forum post)

PvE

Presumably, there is an additional factor when there is a level disparity between the caster and the target, as it has been observered that a significantly higher level player running in a lower level instance experiences greater frequency of resisted elemental damage. The reverse would also be true for a lower level player running in a higher level instance.

From the above quote, a player would require 17 resistance points/level to maintain 100% immunity to a particular elemental damage, on a PvE server.

PvP

From the above quote, a player would require 37 resistance points/level to maintain 100% immunity to a particular elemental damage on a PvP server.

It should be noted that all players are magically balanced to level 101 on the PvP server.

A PvP player only needs to attain sufficient immunity relative to their particular level and not level 101.