Like all the other gems, Emeralds grant bonuses that are related to their color. The green in Emeralds signify the Elemental power of Poison and Pestilence. In Weapons and Shields, it adds bonuses related to Poison and in Armor and Helms, it adds an increase to Dexterity.
When calculating the final damage after the gems have been added, the damage (but not the length) is added up.
The real damage of poison internally is held as damage per frame and duration in frames, in many cases (including gems, skills, items and so on), the true poison damage is actually a non integer number and the shown value is truncated, meaning you can, if the fractions add up, see some "bonus" effects which is in fact not a bonus, just fractions adding up and being shown when the game truncates the poison damage.
Once the final damage has been calculated by adding the Emeralds, it does X damage total, over its Y duration.