When's the best time to email a busy person?
Here's why: many people (myself included) don't get through their emails each day. When the number of emails someone receives each day exceeds their ability to respond to them those emails start to back up and can go unanswered for days. Now, most mail clients show the newest emails first, so new emails actually have a higher visual priority than old emails and will tend to get handled sooner as the recipient races to try to keep up with the inflow of contact requests.
If you get your emails into someone's inbox after they have handled all the overnight notifications, marketing and spam messages, it'll sit as close to the top of their inbox for the greatest period of time and has the best chance of actually getting handled before falling into the bottom-of-the-inbox-hell. Given the variation in times in when people arrive at the office, mornings also tend to be less "busy" (with calls, meetings and the like) and so I'd guess people tend to spend more of their time responding to emails in the AM than the PM.
When's the worst time to email someone? Anytime in the late afternoon into the evening. Those email will get stacked up with all the overnight emails and may be ignored. Even worse, If they are viewed on a smartphone or the like but can't be responded to immediately because the reader is not at the office, they email client will still mark them as "read" and they will effectively disappear into the clutter of the inbox.
(Note, this is all from my own personal experience as both the sender and recipient, so I'm sure there's lots of other opinions on the matter)