A Canary Day is a colloquial expression for a day of immense slothfulness, rest, or otherwise inhibition to perform the daily duties and routine of ones life. Often it is associated with drug use, abnormal sleeping schedules, and containment in a closed space for the entirety or majority of the day.
"I just had a 'Canary Day' week. I was so stressed from last week's work that I just couldn't focus on anything this week!"
Used as a substitute for 'half day' in the context of attending work. The purpose is to be vague, so as to not obligate yourself to actually being present for at least half the work day.
He's taking a partial daytoday, so he'll probably show up at 3pm and leave at 5.