Any client on a wireless network, including clients you don't know about, could be consuming bandwidth. Networks must be protected with WPA2 security. If yours isn't, change the security setting on the access point. If it's already set that way, change the password. Make it a string of at least 8 random characters, including digits and upper- and lower-case letters. The password is saved in the keychain and you don't have to be able remember it; in fact, you shouldn't be able to remember it.
You make these changes in AirPort Utility, if the access point is an Apple device, or in a web browser otherwise.
If the network or the password was insecure, and bandwidth use returns to normal after securing it, you can be pretty sure the problem was caused by intruders.
But intrusion may not be the issue. Most often BitTorrent, iCloud or some other cloud-data application is involved in cases of mysterious bandwidth use by a Mac. If you use iCloud, uncheck at least Photo Stream and Documents & Data in its preference pane and see whether there's any change. If you use third-party network backup software, disable that. If you use a torrent client, remove it.
Otherwise, there's no easy way to monitor network usage per process using built-in tools. If you're an advanced user and you want to try, see the manual page for the nettop(1) shell command. It may or may not provide the information you're looking for.
The third-party products Rubbernet and Little Snitch are supposed to record network usage by processes. I can't vouch for them. Both were available as free trials, the last time I checked. I suggest you uninstall either one when the question has been answered.
