The mysterious man is Maxwell Saxon.
During this time, he's been busy with company matters, traveling back and forth between two cities, so he hasn't had the chance to come see her. However, even though he hasn't come, he's arranged for a flower shop boy to deliver fresh flowers every day.
The day before yesterday, it was baby's breath, yesterday it was blue roses, today it's lilies. Going back a few days, there were irises and roses as well.
In short, he changes it up every day, sending flowers continuously for half a month without repeating any.
And each delivery of fresh flowers comes with a card, on which he pens some words himself.
The content of the cards is quite similar; it mostly shares some of his daily happenings with her.
For instance, he might say he ate something delicious today and promises to take her to try it next time when he's free.
Or perhaps he heard that a certain movie is great, and suggests they go watch it together when he has time.
