Scholastic sanctuary was the idea of giving sanctuary to an individual at a scholastic place. This was a custom in Lyra's world, and Lyra Belacqua was the first child to receive this status from Jordan College.
Certain Latin words had to be said to gain scholastic sanctuary: "Secendum legem de refugio scholasticorum, protectionem tegimentumque huius collegii pro (name of person) nomine reposco". literally meaning "According to the law of refuge of scholastics, I claim the protection and shelter of this college for (name) by name".
The protection from the Magisterium it afforded to both scholars and Lyra was threatened with the introduction of the Rectification of Historical Anomalies Bill, which had its origins in La Maison Juste.