1. Black is a pawn down but dictating play
2. compensation proves enough to draw
Refers to the positive aspects (when they exist) of being material down. Compensation can take various forms: damage to the opponent's pawn structure, control of a colour complex, an initiative, or an attack on the king.
In position 1 (Quang Liem - Carlsen, 2022), black has sacrificed a pawn in return for a lead in development. White is yet to develop the bishop on c1 and rook on a1 and will only be able to do so on a3 after first playing a4.
In position 2, the same game, white has managed to develop his dark square bishop, but the time it has taken has allowed black bring his rooks to the central files and sacrifice with 24... Nxf2!, securing a draw, as after 25. Bc1 (25. RxN Qxe3 -+) Nh3+ 26. Kh1 (26. Kh1 Qg6+) Nf2+ 27. Kg1 white must agree to a perpetual check. Note that while the white bishop finally emerged from c1, the white rook did not have the chance to move from a1.
See: 'Initiative' and 'Colour complex'.