A client can normally join only a server on the same version. Players update automatically and mod authors and plugin developers do not move at the same speed, so a server often runs behind its players. The Via family translates the network protocol so clients of other versions can connect.
ViaVersion lets newer clients join an older server. It is the base the others build on and is the one most servers install first.
ViaBackwards is an addon that does the opposite: it lets older clients join a newer server. ViaRewind extends that to much older clients, including versions from the 1.7 and 1.8 era that many players still prefer for combat.
Translation has limits. Features that exist on only one side cannot be fully reproduced, so a client on a very different version may see some blocks or items replaced with something similar. Use the plugins to widen access, and keep your server current anyway, because the compatibility layer is a convenience rather than a long-term plan.
These plugins can run on the backend servers or, more commonly on networks, on the proxy, so that every server behind it benefits.