The timber-framed buildings are St. William's College. They date from 1465. More information about them can be found on the Jorvik (discovering York) website: Link
When SE6052 : York. located at SE603520 is moved to this square, the story is that "Mad Alice" was hanged here in 1825, apparently only guilty of being 'mad'. The ghost of Alice reputedly drifts along the lane which once was named after her and features in the city's ghost tour industry.