pure in the sense of unmixed: containing nothing foreign, spoiling, or blameworthy
Two settings account for every use of this word. In the instructions for Israel's worship it describes a material refined down to nothing but itself: olive oil beaten and strained until it burns clear in the lamp, and frankincense with no other spice blended into it. In Job and Proverbs it describes people, along with their conduct, their words, and their prayers.
One picture holds both halves together. Something is pure in this sense not because it has been washed but because nothing foreign is in it. That is what separates it from the ordinary worship word for clean (טָהוֹר), which asks whether a person or object is fit to come near God. To call someone pure here is to say no guilt is mixed into him, the way no cheaper oil is mixed into the oil for the lamp.
Job is where the word does its hardest work. Job and his friends pass it back and forth as a claim to be argued: Bildad offers it as a condition, Job presses it as a fact about his own case, and Elihu quotes it back at him. Proverbs then puts a needle in it. Every man's ways look pure to the man himself, and the one who actually weighs them is the Lord.