Used to control the graphical layer priority of the player. 01 will send him behind objects, 02 will send him behind objects and sprites, and 03 will only send him behind sprites.
#$01 is also used to indicate Mario as being behind a net, meaning he'll only interact with sprites also behind nets (indicated by $1632).
#$02 is used when entering pipes and #$03 is used on the overworld and after killing Bowser. Both of these disable sprite interaction entirely.