What is the origin of the term "hit point"?

The terms defense strength points and attack strength points, which were used in old board games or war games, could have eventually been shortened to hit points and then used in other categories, such as role playing games like D&D. Alternatively, the term may have been coined at the time of D&D and then began to be used for the older games for short.

From BoardGameGeek.com:

Naval wargames are notorious for the many-hit-points feature. One of the cool things about tactical naval games is that a ship can take (or inflict) so many different kinds of damage.

Whether the term in reference to games is old as Battleship, can't be determined merely from the quote above, unfortunately.

I don't know if it is significant that the NGram shows the use of the phrase went up shortly after D&D's invention in 1974.

Hit Points as a way of referencing the general remaining health of a person is taken from the game Dungeons and Dragons, originally published back in the '70s. It was the first really popular stat-based role-playing game, and became kind of a touchstone for geekyness.

The idea was that you had a given number of hit points, based on your character class, constitution, and level. When attacked, you lose a certain number based on the power of the attack and a die roll. When/if your "HP" drops to 0, you die.

There are other games that use a "hit point" system these days, and probably were before D&D, but that is the game that popularized the concept. If you hear someone talking about "hit points" in real life, they are making a nerdy D&D reference.