"Poppy was always served after a Feast: it clarified the mind and stimulated the tongue, and made for rich conversation"
Opium Poppies
Creative Commons AttributionOpium Poppies - Credit: SuperFantastic

This line, along with the fact that the smell of the poppy later makes Lyra sleepy, suggests that it is consumed for its psychotropic effects. Poppies are the source of the drug opium, which was very popular in the Victorian era on which this world seems to be based.

Although it isn't mentioned specifically how the Scholars use the poppy, it's hinted that they eat it and so the effects of the drug would probably be fairly mild.