‘Connection via relay’ can be compared to sending a physical letter to someone via a post office box address. The letter will still arrive at receiver but the sender does not know the receiver's real address just the address of the post office box.
Relay is a similar concept… rather than files going directly to the destination they go via a midpoint (the relay server). Why do files get sent via the Relay server rather than going direct?
This happens when the destination is hidden and therefore not known by the outside world i.e. if you have a firewall security setup then the address of your Lima device will not be revealed to the outside world but this means that it is not possible to send your files directly to your Lima - they have to be sent via the Relay server.
The only disadvantage in having your files sent via the relay server (i.e. Relay mode) is that this slows down the transfers. For some files this does not necessarily matter but if you are trying to stream information, particularly video, then having the transfer slowed down by the relay is not desirable.
If you want to read the technical detail behind how we manage to send files to and from your Lima Device while still keeping your system secure you can read the technical details here.
Note that 'Connection via relay' displayed on Lima device(s) in preferences is only about Lima device(s) setup, it does not concern desktop or mobile device(s).