A piece (often a bad bishop, but in your second example a queen) which is doing nothing more than protecting a few squares is often called a big pawn. To be honest, I don't find your second example a real case of a 'big pawn', because the queen can easily move away and do something useful. And, as Dag Oskar Madsen mentions, in the first example the pawn breakthrough is big, not the pawn itself.
In the position below, the white bishop is a typical example of a big pawn, because of Black's dominance on the dark squares:
[FEN "r4r2/5pkp/1q1pb1p1/2p1n3/2P1P3/1P3P2/2BN2PP/1R1Q1RK1 b - - 0 1"]
The term big pawn is usually used to mean an ineffective bishop trapped behind its own pawns. An example from the game Charousek-Maroczy, Budapest 1895:
[FEN "6rk/1pp3p1/1r3p1p/p3nP1P/P1PpP3/1P1P4/2B1K1R1/6R1 w - - 0 1"]
In this position, the white bishop is just doing the work of a pawn and doesn't have any bigger prospects.
As mentioned, the first one refers to the amount and importance of pawn play throughout that game.
The second example seems to be making a joke about how the Queen is so ineffective in its position that it might as well be a pawn. If you play through the puzzle you see that it is not able to prevent the sequence.