The answer to this is a little convoluted and the answer is just what is "believed" to have been the reason behind the scoring numbers, but since tennis is a game that dates back to the 19th century, it's tough to know for sure.

Anyway, here goes...

Think of a clock face that is divided up into quadrants - which would give you the 15, 30, 45, and 60 intervals. The problem with using that to score tennis games though, is that to win a game, you have to win by 2 points if the score reaches deuce (40-40 or "40 all"). So it is believed that the first 3 points would advance the hand to 15, 30 and 40 - and then the next 2 points would advance the hand by 10 minutes - first to 50, then to 60 - still keeping the game finished at the 60 mark. If the (serving) player failed to win 2 points in a row after deuce, the hand would move back to 40 and the score would be at deuce again.

See here for some additional theories behind the scoring nomenclature.