"pick up" in this case means to improve on what it was before. The clue is that up until that point the day had been awful.
There are other meanings of the phrase, such as:
"My usual pick up time is at 8am" - someone will come in a vehicle and collect me at that time.
"Pick up that piece of paper!" - literally pick up some paper lying of the ground.
"The train will soon pick up speed" - it will start slowly but get faster (this is like the day)