By moving his Queen off of the d-file, White completely surrenders any attempt to recover his d-pawn, intending perhaps a later c3 to encourage dxc3 when Nxc3 develops the Knight with control of the center. Meanwhile, the Queen protects the e-pawn and threatens to push it forward with 6.e5, when the Black Knight at f6 will not have a comfortable retreat, especially since 6....d5 is not possible due to 7.exf6+. But White's plan is not the best. The standard moves here are 5.O-O, 5.e5, and 5.Ng5, all of which do a better job of protecting the e-pawn (in the case of 5.O-O, indirectly) while preserving the Queen's options.
Black prevents the immediate e5 and opens the way for his light-squared Bishop to go to g4. But there may have been no need to prevent White from playing 6.e5. In fact, Black seems to dobest to encourage it so as to take advantage of the aligned White King and Queen along the e-file. In the game Pietzsch-Masieev, Correspondence 1967, Black played 5....Bc5! 6.e5 O-O! 7.O-O (White cannot take the Knight: if 7.exf6? Re8! pins White's Queen and gives Black a deadly attack after 8.Be3 dxe3 -+) 7....d5! 8.Bb5 Ne4 =+ 9.Nbd2 Nxd2!? 10.Qxd2 Qe7 11.Bxc6 bxc6 12.Nxd4 Qxe5 13.Nxc6 Qd6 14.b4 Qxc6 15.bxc5 Qxc5 16.Bb2 Bf5 17.Rac1 Rab8 18.Qd4 Qxd4 19.Bxd4 a6 20.Rfd1 Rfd8 21.f3 Rb4 22.c3 Rc4 23.g4 Bg6 24.Be3 c5 25.Kf2 f6 26.Kg3 Bf7 0-1 No doubt Marshall would have preferred this line if he had seen it.
Smirka pursues a strategy familiar from the Gambit Line of the Perreux Variation of the Two Knights Defense. But if he had wanted to play in this fashion, he could have simply played 5.Ng5 Ne5 6.Bb3 h6 7.f4 hxg5 8.fxe5 Nxe4 when either 9.Bd5!? or 9.Qxd4 leads to interesting play. Note that if 6.c3?! Bg4! keeps the tension in Black's favor. Perhaps best at this point is 6.Bg5 Be7 7.Nbd2 followed by O-O-O, when at least White will have a speedy development to give him good chances of regaining the d-pawn.
Marshall seeks to gain time in development and the initiative, even at the risk of returning his extra material. The straightforward 8....hxg5 9.fxe5 dxe5 10.Bxg5 (not 10.Qb5+?! Nd7) gives White some play along the f-file and a continuing initiative, but Black's extra pawn should tell in the end. Marshall, however, always preferred the initiative to material.
What was Marshall planning to do if White snatched the b-pawn? Likely his plan was simply to secure a speedy development to create chances for attack. Play might have gone 10.Qxb7 Rb8! 11.Qxa7 hxg5 12.fxe5 dxe5 13.Bxg5 Bb4+ with a big lead in development. The position, though, is at least materially better for White than what Smirka achieves in the game. Therefore it was likely best to grab the b-pawn. It is easy to sympathize with Smirka's suspicion that the crafty Grandmaster must have had some swindle in mind if he did so. But you always need to trust your own view of the matter, rejecting any thought that your opponent might know better.
White hopes to keep Black's King in the center with his sacrifice. But it turns out that White's King is more exposed in the long run. But 14.Nxc3 Qe7 is certainly not much better.
The Queen dominates the White position and keeps the enemy King confined to the center of the board (beginning players often forget that you cannot castle over a square controlled by your opponent -- and the Queen at d3 controls both d1 and f1), where it will be subject to a devastating attack. There is no hope for White at this point, but he speeds the end by helping to open up the e-file. A better defense may have been 18.Bxf6 followed by Rd1, though White already has a losing material deficit.
Clearing the e-file and threatening mate on e2.
White has run out of checks and now the e-file opens completely, leaving his King naked in the center. The rest is ugly for White.