Why do they say "love fifteen," in tennis?

"Love" is one of the ways you can read the number "0". So "fifteen love" means "The score is 15-0".

There are many theories about its origin. One is (taken from Wikipedia - but you'll find this anywhere):

The origin of the use of "love" for zero is also disputed. It is possible that it derives from the French expression for "the egg" (l'œuf) because an egg looks like the number zero.

According to Oxford,

It seems to have been adapted from the phrase 'to play for love (of the game)' (i.e. to play for nothing). Although the theory is often heard that it represents the French word l'oeuf, meaning 'an egg' (from the resemblance between an egg and a nought) this seems unlikely.

"Love" means zero. In tennis, the server's score is given first, so "love-fifteen" means the server has no points, the opponent has fifteen.

The score in a tennis game progresses from love to fifteen to thirty to forty to game. If both players achieve forty then it's called a deuce. A player must win a game by two points, so the player who scores the next point is said to have "advantage." If the opposing player scores the next point, they go back to deuce.

It's a quirky scoring procedure. Its roots derive from French, not English, so I feel within my rights to declare ignorance without penalty at this point. :-)

In tennis, scoring is a bit...unorthodox. In particular, love is equivalent to 0 points scored in a game, while fifteen actually means you've scored one point.

Love fifteen effectively indicates that the serving player has 0 points, while the receiving player has one.