it is difficult to define, basically are you driving the game and forcing moves or are you forced to constantly respond to your opponent.
Tempo?

That's initiative, not tempo.
A lead in tempi is often realized during the opening -- when an opponent moves a piece twice, either through carelessness or by being forced to or makes an unnecessary pawn move while you continue to develop you gain tempi and a lead in development as a direct result.

I look at tempo in this way. If i get my men out faster then my opponent that gives me an attacking advantage because i can start to work on getting his king.
Same thing applies if your trying to get someone to lose a move (tempi) basically so you get a lead in position.

Tempo is time..You gain time by making a good move, sometimes in response to an oppponent's weak move.

a tempo= 1 move. If you make your opponent do a bad move. You are considered to have gained a tempo.

It essentially is a move. This is most important when you look at pieces developing. This is why it is taboo to move the same piece repeatedly during an opening while the other player developes.
This is different than iniative which is which player is commanding the series of moves and which player is responding. Iniative is spent when a player no longer forces responses from his opponent. Tempo is never "spent" in that same manner. Rather this is used to force an iniative.

What is tempo?
Tempo, is VERY important. In the beginning of game, white has 1 tempo. So he has first strike. In some games, black can win the tempo from white and black would have first strikes. Or, white can win 2 tempo from black. Never waste tempo. if your wasting tempo, your like doing this:
What is tempo?