Harrenhal aka Black Harren's folly/Black Harren's monstrosity is the largest Castle in the seven Kingdoms.
It was build by the Last Hoare King, Harren the Black, who was King of the Rivers and Isles.
It is located near God's Eye in Riverlands. You can see it on the map here:
Before the Castle war built, the Iron Kings of Rivers and Isles used to hold a small castle near Fairmarket as their seat. Harren however wanted something grand. It took forty years to build the Castle and thousands of men died slaving away to build it. The venture beggared both of Harren's Kingdoms (Riverlands and Iron Islands). The same day as Harren moved in the Castle, Targaryen invasion begun. Harren thought his Castle was invincible so he refused to surrender to Aegon I. Aegon burnt the Castle and Harren burnt with all his sons and family.
The Castle ever since has a sinister reputation. Every House which touched it perished.
The Reason why Arya along with Other Prisoners is brought to Harrenhal is because that's where Tywin Lannister made his headquarters after Robb Stark defeated Jaime in the Whispering Woods. Tywin retreated from Ruby Fork and positioned himself at Harrenhal so that he could be in a defensible position and close enough to defend King's Landing itself. To maintain the Army, Labour was needed. So the Villagers were rounded up and brought there to serve the Lords and Knights and their retinues.
Prisoners of Harrenhal aren't Criminals. They are just people of the losing side and they have been turned into forced labor for their captives. That's why they don't get a choice, they have done no crime other than being who they were.