A little context for this: it is essentially a symbol of Britain. The unicorn represents Scotland, the lion England. This staircase was built in 1690, at which point the Scottish and English crowns were still separate offices but had been held by the same succession of monarchs for quite some time (with a break for Cromwell and co), and the idea of uniting the two permanently had recently been sort of semi-formally agreed upon. Opposition from both sides of the border meant that it didn't happen for another 17 years, an economic disaster for Scotland, and some repression of churches, but the idea was there. This same arrangement of unicorn and lion still flanks the coat of arms of the UK today. The staircase is, effectively, a representation of the political union that was yet to come
Wales and Northern Ireland, unfortunately, do not get as much representation. Wales doesn't actually get any. I know why it is like that, historically, but come the fuck on. We're already dividing the shield into four parts and we have four constituent countries. We should stop doubling up on Scotland and England
Also Glasgow University's main building is gorgeous in general. The staircase actually pre-dates it by almost 200 years, but was moved to its current location as part of the main building when that was built