Discreet
On a gay profile, a man who wants sex with men to stay secret: closeted, DL or married, usually with no face pics and no hanging out.

Discreet, on a gay profile, means "nobody can know about this". The man may be married, closeted, living with a girlfriend, in a job where he can't be out, or just very private; either way he wants sex with men to stay invisible. In practice it comes with a set of rules: no face pics, no hanging out, no saying hi in public, and usually no hosting.
It is a code word more than a description. Everybody is discreet in the dictionary sense; on the apps "discreet" is a status, close kin to DL and closeted, and sometimes a polite way of saying "married".
How it is used
You see it in headlines and bios, often in a cluster:
- Discreet, NSA: sex, then silence.
- Discreet, masc, str8-acting: the classic DL profile.
- Discreet only / be discreet: the other man must keep the secret too.
- Discreet, can't host: there is someone at home.
A headless torso as the profile photo is the visual version of the same word.
Discreet, DL or closeted
The three overlap but are not the same. A closeted man hides that he is gay; a DL man may not consider himself gay at all and lives as straight; "discreet" is the request both of them make on the apps. Plenty of out gay men also write "discreet" simply because they don't want their sex life to become group-chat material, which is fair enough.
The gay take
For some men discretion is a matter of safety: in many countries, and in many families, being found out still costs jobs, homes or worse, and the apps are the only place they can be themselves at all. For others it is a convenience. The community has mixed feelings: many out men are happy to keep a secret; plenty are tired of being somebody's secret, and some read "discreet" next to "masc only" as a sign of shame they would rather not share. The word survives because the need for it does.
No face pic means you don't really know who is coming. Tell a friend where you're going, and meet somewhere you can leave.