What does the x1 elemental damage mean?

An elemental weapon actually usually shoots normal bullets, that are exactly the same as that of a normal gun. However, sometimes they trigger an elemental effect, or "proc" (short for "programmed random occurrence" or "procedure"). When this happens in addition to the bullet damage, the elemental effect and damage is added. These procs can trigger with varying intensities, from x1 to x4, as seen on weapon infocards. Different weapons have different proc chances for each of these elemental multipliers.

Whenever a weapon procs, a certain amount of elemental damage is added based on the current element's damage multiplier:

Element Damage Multiplier

Incendiary 60%

Shock 100%

Explosive 150%

Corrosive 40%

For example:

• if a 100 damage x1 incendiary repeater procs x1, this will add a 1x incendiary damage multiplier (60%), dealing an extra 60 damage.
• If a 100 damage x3 explosive sniper rifle procs x3, this will add a 1.5x explosive damage multiplier (150%) dealing an extra 225 damage.

Taken from here and is also worth looking at for more information regarding specific weapons and their elemental effect.