From what I've experienced, it seems to effect the amount of time that an elemental effect (Incendiary, Shock, Corrosion, Blast) will take effect. So if you have a x1, you have a chance to proc the effect, x2 a higher chance, x3, and x4 are almost guaranteed. At least that seems to be the concensus on the forums I've visited, and is confirmed by the (admittedly, possibly wrong) Wiki.
I also think it effects the amount of damage that is applied for DoT effects such as Corrosion, and Incendiary. However, I've found no concrete numbers to support that, just speculation that it's the weapon's base damage time the effect number, dealt over time.
For example, an Incendiary x4 SMG shoots a bullet, lights the enemy on fire, and does 600 base damage. The enemy then takes 600 damage x4 over time, in effect taking a total of 3000 damage.
(600 + (600 x 4) = 3000
I don't know if that's correct or not, because it seems to me, that would make ANY DoT weapons far superior to their normal counterparts that just deal their base damage, almost no matter how high their base is... the other side of the coin is... there are a TREMENDOUS amount of Elemental weapons in the game. I seem to get more elemental weapons than regular weapons TBH, and also I play a Siren most of the time, so SMG's with elemental effects are superior to any weapon out there, the way I've built her up anyway. My Hunter, who is a bit lower level also uses them, but not as effectively as she seems to, which may indicate that the theory above on it actually effecting the amount of damage is completely false.
Also there are some elemental weapons with red text that guarantee an elemental effect, but also have multipliers. This points twoards the theory above being correct.
So... in closing... the only answer that anyone has given is pure speculation, unless you take the Wiki as gospel. So I just spent 10 minutes typing, and still didn't answer the question definitely, wasting your time, and mine... but hey, I was entertained for that 10 minutes looking for answers! It'd be really nice if someone who plays with a Gearbox employee to ask them that question, and get one of 'em to post what the true answer is.
http://borderlands.w...om/wiki/Weapons
War is In Your Blood, the red text on that gun seems like it could be pretty nifty...