An e-mail that one mate writes to another mate that is intended to be read as an accompaniment to his/her breakfast. It is typically written late at night and may include amusing anecdotes or newsworthy items pertaining to the writer's personal life. It is usually relatively short in duration and is written purely to entertain, amuse and/or encourage the reader as he/she starts her day. Also referred to as "breaky email", it must not contain angry rants, tedious stories or non-sensical ramblings.
Jon is tired at the end of a long day and is anxious to get some sleep. So he says to his mate, "Oi! Will you send me a breakfast e-mail so I've got something to read whilst I eat my toast with vegemite in the morning?" And Jon's mate replies, "No problem, eh?"