Chess masters- how they think about material

I don't know about that.  Most lower-rateds tend to overlook hanging pieces a good percentage of the time.

Wafflemaster makes some excellent posts in this thread, so I would take a good look at what he wrote.

Position tends to matter much more the higher rated you get, but so do piece values! This is because a master+ player is better at converting smaller advantages (position, material) into larger advantages and then into a win. If a high rated player is giving away material (or so it appears) it is either because they feel there is significant compensation (position/a great attack) or because it is a conceiled trap (to the untrained eye).

All true.  Then again, in order to "take anything their opponent gives them," they have to see it first! lol

An attacked piece doesn't necessarily have to be defended: not if you can move so that if the enemy carries out his threatened capture, he suffers worse in return. I call this technique "indirect defense." Obviously it is liberating if you don't have to always tie yourself down in defense, but can use your mobility for offense instead. So if attacked, the "automatic" defense is not my first impulse, but my last resort.

pawns are usually worth 3 tempi  (3 moves)

so they might sack a pawn to get 3 moves of attack / initiative.

also you have to realize that GMs study chess 8 hours a day.  they are total nerds and losers and have no lives except to play a boardgame. 

so they have all their variations planned out when they start a game.  they usually have the line worked out and know the sequence from start to finish. 

...bump... that

Material is potential.
In itself worth nothing till put in effect.
You have an energy budget worth of things like material, tempo, activity and king safety that you can invest and interexchange.

A GM is extremely well trained to feel and understand what matters when.

When your position is tied down and some pieces are completely inactive, you are essentially playing down material. Maybe you can trade one for the other.
Maybe an opponents piece is extremely active. Might be worth investing a more valuable but poorly placed piece of your own to get a better playable position and up your chances. 

It's a big part of what makes chess interesting. And so extremely hard.

They can take the pawn but is it really good? If white can recapture with a piece making it centralised?