A State is an ongoing effect on a creature, usually in combat. The effects vary depending on which state it is, ranging from suffering damage to complete immunity to damage. The duration of a state can vary and a creature may have many different states on them at any one time, though some states can only have one copy present on that creature at the time.
There are a number of common States, where many different spells can apply the same State. Usually applying the same state twice on a target will refresh the state or increase the number of stacks of the state.
A number of States are able to stack their effects. This is indicated by 3 circles next to the state's name within the UI. The current "stack size" of an ongoing state is shown as a numeric indicator on the icon.
If a stacking state is applied from multiple sources at the same time the state's effect will be increase by the total combined level. Depending on the state, applying more stack will also refresh the duration of the state.
A number of States have a scaling effect based on the level of the spell which applied them. With Elemental Spells, the weakest version of the state is applied at level 0, while the most powerful version is applied at level 200. Some states only have a single level, such as stunned.