The blackboard is a minor activity in the series.
After the deadline of each Palace heist in the story, the protagonist will be able to draw the Phantom Thieves logo on the blackboard in his classroom after school, which will grant a reaction from his classmates, depending on the current Palace arc.
Although drawing on the blackboard generally does not affect anything within the game, at one point, the protagonist can receive a Social Stat boost. After Kunikazu Okumura's change of heart, or starting from 10/31, the protagonist can improve his Guts stat by 1 note. It only works once.