Goneril has fallen in love with Edmund. They are plotting to assassinate her husband Albany so that they can marry. This would elevate Edmund to be co-ruler of England.
In Act 4, Scene 2, there is a brief encounter between Edmund and Goneril in which they come to an understanding that they will marry if they can dispose of Albany. Goneril's speech to Edmund ends with a few significant lines:
Decline your head: this kiss, if it durst speak,
Would stretch thy spirits up into the air:
Conceive, and fare thee well.
Yours in the ranks of death.
My most dear Gloucester!
When Edgar kills Goneril's servant Oswald in Act 4, Scene 6, Edgar gets possession of an incriminating letter from Goneril to Edmund which reads:
Let our reciprocal vows be remembered. You have many opportunities to cut him off: if your will want not, time and place will be fruitfully offered. There is nothing done, if he return the conqueror [in the battle with the invading French army] then am I the prisoner, and his bed my gaol; from the loathed warmth whereof deliver me, and supply the place for your labour. "Your--wife, so I would say--affectionate servant, "GONERIL."
When Edgar turns this letter over to Albany, Goneril, who has already poisoned her sister Regan, commits suicide, and Edgar kills his treacherous half-brother Edmund in a duel. Both wicked sisters Regan and Goneril were in love with Edmund, presumably because he was as wicked as they were. Regan was a widow because her husband Cornwall had been killed by a servant who was trying to prevent him from blinding Edgar and Edmund's father, then Earl of Gloucester. Goneril poisoned Regan because she was afraid she might marry Edmund before she could managed to dispose of her own husband Albany.