Discord is free to use, and doesn't run advertisements, so it may be unclear on how they make money. Are they selling data? Are they only subsisting off of investment funds?
Well, they are not selling data, that much is clear. However, much of their initial money has come from investment. According to CrunchBase, Discord has raised over $250 million from investors. But this can't keep them going forever.
Discord Nitro is one way that the company makes money. This optional service unlocks small benefits such as a boosted file upload limit, animated profile images, and more. For a time, it also included access to Discord's game library, but Discord removed this feature.
If you're a dedicated Discord fan, you may want to purchase some merchandise to show your support out in public. Discord sells shirts, hoodies, and hats, so you can rep your favorite chat app IRL.
Discord is always working on new features, so there may be more revenue sources on the horizon, whether they get money out of users, or from developers of other software.