People
We exchanged significant glances. At least, I gave him a significant glance and he looked like a stuffed frog, his habit when being discreet.
— P.G. Wodehouse • How Right You Are, Jeeves

Behind the line May contain spoilers.
Our reading
An editorial interpretation.
The narrator jokes that he shot a meaningful look and got back a face like a stuffed frog, which is apparently how the other man looks when being discreet. The humour is in the absurd comparison and the narrator's earnest confidence.
Context reviewed