Odds are it's this paragraph
By uploading, distributing, transmitting or otherwise using Your Content with the Service, you grant to us a perpetual, nonexclusive, transferable, royalty-free, sublicensable, and worldwide license to use, host, reproduce, modify, adapt, publish, translate, create derivative works from, distribute, perform, and display Your Content in connection with operating and providing the Service.
It's a pretty standard clause in Terms of Service. Checking three big services (Facebook, Twitter and Reddit), all of them have the same clause, almost verbatim. I'm not even close to a lawyer, but as I understand it, it's mainly an ass-covering clause that allows them to actually provide their product. Otherwise you'd have to give permission for them to upload every message, picture, file etc to their servers, store it, send it to others in the chat etc.
This is correct, and every major service has a similar clause.
When you upload, say, an image to our Service, you must
- Give us the rights to distribute it to others
- Allow us to modify it, by cropping it or compressing it
- Allow us to create derivitive work from it, again by cropping or compressing it
- Transfer/sublicense this license, if Discord were to ever own an international subsidiary for example.
Note that the last sentance clearly says we only have these rights in connection with operating and providing the Service, meaning these rights are only given to us in the context of making Discord work, we can't steal your stuff and use it on something not related to providing the Service.