Learnings: Trust and Oathkeeping
Oaths relied on trust, but it was hard for Christians to see heathens as trustworthy. If the Vikings swore on a sacred object, as could have served this bowl, they couldn't be trusted to abide by tha oath because they did not share the Christian faith. On the other hand, if they were allowed to swear on their own sacred objects (a ring, for example), the oath would be committed to false pagan gods that Christians referred to as demons.
So the best way to trust each other, especially from the Christian point of view, was to share a common sacred reference. Therefore, conversion and baptism of the defeated heathens was the best guarantee for the creation of this common ground, and the condition for mutual trust. This was what happened to Guthrum and his men after their defeat. In order for Guthrum's oath to Alfred to be considered valid, he first needed to convert to Christianity.