Learn English – Where did “the price of tea in china” come from

"To bite the dust" means to die or to fail (see e.g. Wiktionary). Picture someone falling down, wounded or dead, quite literally biting the dust (soil, ground, earth). Etymonline says that the first recorded appearance of the phrase is from 1750. The Phrase Finder supplies it as follows:

The earliest citation of the 'bite the dust' version [of the earlier phrase 'lick the dust', from the Bible] is from 1750 by the Scottish author Tobias Smollett , in his Adventures of Gil Blas of Santillane:

"We made two of them bite the dust, and the others betake themselves to flight."

[...]

[Samuel Butler's 19th century translation of Homer's The Iliad] contains a reference to 'bite the dust' in these lines:

"Grant that my sword may pierce the shirt of Hector about his heart, and that full many of his comrades may bite the dust as they fall dying round him."

Whether that can be counted as an 8th century BC origin for 'bite the dust' is open to question and some would say that it was Butler's use of the phrase rather than Homer's.

It was first used as an interjection in the 19th century: “They marched, and I amongst them, to face the enemy – heads up – step firm – thus it was – quick time – march!”

Then, at the beginning of the 20th century, it began to be used adjectivally, as in: “He was always right on the job, and looking ‘heads up’.”

Then, around the late 70s, it became a noun, probably through shortening of phrases like “heads-up alert” into “heads-up”: “It is regarded as being a heads-up on a sale.”

^{Source and references: the Grammarphobia blog}