Hoxuin is an emissary of death, gathering the souls of those who die and guiding them into the afterlife. Many asari believe that a person is only truly dead once none remain who remember them. Given the extremely short lifespan of salarians compared to asari, there were suddenly, post-contact, many beings whose lives weren't being forgotten for centuries beyond the time of their passing. This supposedly angered Hoxuin, who now wasn't able to collect as many souls as she once could.
Some accounts argue that she took issue with the fact that shorter-lived species were being deprived of their afterlife for what was (to them) multi-generational spans of time, which she believed was an injustice; others claim that she simply became frustrated at not being able to do her job as efficiently as she had. All stories agree that she eventually had an idea to tip the balance back toward how things had previously been.
Hoxuin thus spent her free time (and there was now more of it) sneaking into the sleeping quarters of asari, laying her hands upon their scalps and quietly removing their memories of any non-asari who had died, in an effort to free up souls. In asari terms, she essentially began killing those people in the minds of those who'd known them.
To quote Mirala T'Narf:
"Even now, those occurrences when an asari realises she can't remember the eye colour of the turian who lived next door to her as a girl, or the name of the quarian who smiled at her whenever she passed, or any number of other details that are naturally lost to the winds of time - which can occasionally be quite distressing, since that lost memory may have been the last trace of that person's existence - this is sometimes referred to as Hoxuin's Curse."