DPS, or Damage Per Second, is a measurement of a weapon's strength. It shows how much damage a weapon can deal, on average, in a second. The higher the DPS, the better the weapon.
You can count DPS by multyplying attack and speed (how many attacks per second). For example if you have a 2 damage weapon that attacks twice per second, that weapon has 2 * 2 DPS = 4 DPS. But, DPS doesn't show how much damage you deal exactly per second. For example, if you have a 8 damage weapon that attacks once every two seconds, it means your DPS is 8 * 0,5 DPS = 4 DPS. But the weapon itself deals eight damage every two second, and not four a second.
N.B. DPS is not an abbreviation of damage per strike.