Each weapon has a damage type. Each damage type appears to have a 'proc effect' that can occur. There are instances of this not being listed in the weapons details (right click and examine) so please check carefully. If the weapon has the damage type and has +Effect Strength (which you want anyway), this will definately proc though, so its not too large a consideration. It looks to be a pretty low base chance to proc for me at any rate, something in the region of 1-2%.
The effects are as follows....
Fire - Chance to Ignite (burn) - Target loses 5% of its total HP per second for 5(?) seconds.
Toxic - Chance to Poison - Target is unable to heal and receives X damage per second for 5(?) seconds.
Electric - Chance to Shock - Target is unable to cast spells or use abilities.
Physical - Chance to Stun - Target is unable to move, cast spells or use abilities.
Spectral - Chance to Phase - Target takes 50% increased damage and does 50% less damage for 5 seconds.
There is no cooldown on the proc, and you can chain proc a mob.
The procs DO NOT STACK, but the duration is refreshed when they re-proc. Therefore if ignite occurs twice within its 5 second duration, it will not do 10% damage to a mob per tick, it will just refresh the duration on the 5% damage ignite already on the mob instead.
There are various modifiers that effect this proc chance, I will go into more detail on that later.
Various skills and abilities can cause these effects to occur, and as far as I can tell, the skills damage type will always correspond to the effect its creating. For example, if you have a skill that poisons a target, it will do Toxic damage rather than Fire.
You can add either Elemental Damage or Elemental Strength to weapons via mods.
Elemental damage comes in the form of +X% Toxic/Fire/Physical/Electric/Spectral damage mods (eg +16% Fire damage).
Elemental damage will add X% of your weapons damage to your weapon on top of whatever damage it already does.
This extra damage comes in the type that the mod suggests. (eg putting a +5% Fire damage mod into a 100 Spectral damage weapon will make it do 100 spectral damage, plus 5 fire damage on every hit).
If your weapon has +Effect strength on it, but no corresponding damage type, then it appears that putting a +X% Toxic/Fire/Physical/Electric/Spectral damage mod into it will also give it a chance to proc the corresponding effect. (Further Testing needed!)
Elemental Strength comes in the form +X Effect Strength (eg +15 Ignite Strength)
This mod increases the chance for that effect to occur.
At low level even small amounts of this make a noticable difference. Using the Fawkes Gloves (+115 Ignite Strength) with a +48 Ignite Strength weapon, I proc ignite on around 75% of my attacks.
You can only add this chance if the weapon already does the corresponding damage type.
If you add +X Effect Strength to a weapon with the wrong damage type, it will have no effect (believe me, 30 minutes of beating on a regenning mob with a low level Fire weapon with +Phase Strength is fairly conclusive).
To ensure a weapon will proc the effect you want, it needs to have both the damage type, and some effect strength (or at least the effect listed on its details). Otherwise it may not proc at all. This can either be on the basic weapon, or added by a combination of mods it seems