Pawn structure. Giving up a pawn to double opponent's pawns and/or break an opponent's pawns into many pawn islands can justify dropping a pawn.
Things that can be compensation for a pawn
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I also believe an octopus is good compensation for a pawn
any piece you want
A first-round draft pick.
Active play, initiative, trapped piece, space, development, octopus, control of open file. Add on to that