All feed readers talk to other machines to get the feeds you're reading. TTRSS is just fetching them and storing them locally regularly instead of just when the client is running. I don't remember whether or not TTRSS has a reader interface or whether you need to use a client to talk to it.
There are local readers, that fetch the feed directly from your device, but many use backend servers for the feed fetching. There are a handful of possible reasons:
Cross-device syncronization.
Save battery by checking on the server and only waking the device with a push notification when there are actually new items.
Obey platform background activity restrictions (especially on iOS)
Privacy by hiding your IP from the feed operators.
Avoid missing items on busy feeds when your client goes offline by checking constantly from the server.