Your washing machine could be sending 3.7 GB of data a day — LG washing machine owner disconnected his device from Wi-Fi after noticing excessive outgoing daily data traffic

if your switch gear will mirror traffic, then push the traffic to a switchport with a PC running software like wireshark/tshark/tcpdump or your fav. packet sniffer of choice. different setups (integrated wireless, fibre, etc) will require various configuations to packet capture properly,, but you can always find a way of observing traffic - even if you have to use an old hub (not a switch) as a last resort and just flood the traffic to your monitoring device.

once you have a packet trace, things get fun. if the traffic is in the clear (not encrypted) you get all the goods. if its encrypted (and you cant man-in-the-middle attack the crypto session) then, at the very least, you get patterns, timings, IP endpoints, etc...

on higher end switch and router gear (and some open source consumer routers) its pretty easy to sniff traffic and a great learning experience, not to mention the ability to monitor traffic gives you insight into what devices are doing "things" on your network. highly recommended playing with it on a spare laptop to get some experience with it.

Intrusion Detection / Protection Systems often make use of this type of traffic visibility. so do ISPs (and others) for various purposes, of which some usecases are highly privacy unfriendly.

edit: fixed a few obvious typos and added the IDS stuff.