The pity timer works on a scale that resets as soon as you open an legendary. So each pack you don't open a legendary, your chance of opening a legendary in the next pack goes up. Once you open a legendary, the pity timer resets and your chance to open a legendary in the next pack goes back to the base chance of 5%.
So when people say they've "hit their pity timer", they just mean their chance of opening another legendary from that set is now as low as it can possibly be.
Sorry if this has been answered already, but dos the timer work across all pack types, or is there a separate timer for each?