When I first started to review this message board about 9 years ago I had no idea what was meant by a tempo run. Now I understand why. A tempo run, like running itself, is very individual or personal.
The dictionary says that tempo means pace or rate of activity.
I trained with Hungarian Coach Mihaly Igloi in the mid 1960s Every run we made from 100 yards on up had a tempo and he used the term repeatedly.
He had 2 leg actions (swing and speed) and many tempos such as easy, fresh, good, very good, hard, very hard, all out etc. He once called out to me in the middle of a marathon race I was running to switch to very hard speed tempo for 60 yards.
Coach Igloi's athletes set many World, Hungarian, U.S. and Greek Records.