To say something drily is to say it in a flat voice that hides the joke. No smile, no wink — you either catch it or you do not.
The word lives in the dialogue tags of novels: he observed drily, she remarked drily. What it signals is dry humour, the British speciality of delivering a joke as though reading out the weather, where half the comedy is in the deadpan. The spelling is worth noticing: drily is the usual British form and dryly the usual American one, and both are correct. A literal sense of without moisture survives, but it is rare enough now to read as a pun.
1adverbdrilyIn a flat, deadpan way that hides the humour.
“Marvellous, he said drily, and turned the page.”
Also accepted in games: dryly
dryly comes from dry + -ly.
Etymology from Wiktionary, CC BY-SA