I did not know that yesterday!

I started with a Google search on "tennis scoring." After some digging around, I found two possible answers.

The first mention of tennis scoring was on the Lawn Tennis Association web site. On the Origins of Scoring page, we learned that the unusual scoring system has medieval and French roots.

The site goes on to state that the system may be based on the presence of a clock face at the end of the tennis court. A quarter move of the appropriate hand was made after each rest, with the score being called as 15, 30, or 45. As the hand was moved to 60, this was the game. This didn't explain a score of 40, however, so I continued on.

I then found another possible explanation on The Straight Dope.

Tennis scoring has its origin in medieval numerology. The number 60 was considered to be a "good" or "complete" number back then, in about the same way you'd consider 100 to be a nice round figure today. The medieval version of tennis, therefore, was based on 60 -- the four points when 15, 30, 45 (which we abbreviate to 40) and 60, or game.

Although neither of these answers is definitive, it was the closest I could come to acing the question.