Learn English – the origin of “when the chips are down”

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.

One of the colloquial definitions of grind is (from the Oxford English Dictionary):

Steady hard work; labour of a monotonous kind, esp. close and hard study; an instance of this, a dull and laborious task.

The first written use of this is:

1851 B. H. Hall Coll. College Words, Grind, an exaction; an oppressive action. Students speak of a very long lesson which they are required to learn, or of anything which is very unpleasant or difficult to perform as a grind.

So the grind of one's day would be the daily, monotonous work that one has to do. It is more common to refer to this as the daily grind.