What exactly is hosting?

I see a lot of stuff on self hosting vs Bitwarden hosts, but nothing that tells me exactly what the host is doing? Can I still get passwords off my iPhone if I can’t connect to the host? Is the host only necessary for syncing across platforms? What happens if my internet connection is down, but I add a new password on both my desktop and phone? (e.g., the cable modem is down and I’m trying to set up a new one, which needs a new password before I can get it to connect).

If I decide I just need it on my phone, which has iCloud backup, do I need hosting?