If I block someone on one server, they are blocked on all servers for me. If some server I am in has custom emojis and stickers, and I am a discord nitro subscriber, I can reuse those emojis and stickers by posting them on other servers. Other users on that other server can see them, but cannot use them. If i change anything on my profile, it will be reflected on all servers.

There are probably tons of other cross-server relationships that I forgot to mention, simply because I only listed the first few that came to my head.