I found this notice and looked across the cloisters to see one covered over section.
And below is the view from the other side.
Their website says it is quite recent: 1820s. They made a mark at noon when the Sun was highest in the sky on summer solstice. The mark is on the floor.
They drew a line between the two. On any other day, when the Sun hits the line it is noon. Watches and clocks can be set by this. The website says this was necessary because devices were less reliable in those days. This was still before train timetables so there wasn't a standard time across the country. This fixed local Durham Mean Time.