To say that something or someone is "the bane of my existence" means that the person or thing is a constant irritant or source of misery. As a cliché, "bane of my existence" has lost its edge to a large degree over the years, and today is most often applied to something that may profoundly annoy us but is certainly bearable... "Bane of my existence" is now almost always used in a semi-jocular, "what are you gonna do?" sense.
But "bane" was once a very serious word. The Old English "bana" meant literally "slayer" in the sense we now use "killer" or "murderer." Early on, the English "bane" was also used in the more general sense of "cause of death," and by the 14th century "bane" was used in the specialized sense of "poison," a sense which lives on in the names of various poisonous plants such as "henbane" and "wolfbane."
From this very literal "something that kills you" usage, "bane" by the 16th century had broadened into its modern meaning of "something that makes life unpleasant, a curse."
