Any client on a network, including wireless clients you don't know about, could be consuming bandwidth. Wi-Fi 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, Dropbox, or some other cloud-data application is involved in cases of mysterious bandwidth use by a Mac. If you use iCloud, uncheck at least iCloud Drive in its preference pane and see whether there's any change. If you use third-party network backup or file-sync software, disable that. If you use a torrent client, remove it.
Otherwise, if you're running OS X 10.9 or later, you can see which processes are most active on the network.
Launch the Activity Monitor application in any of the following ways:
☞ Enter the first few letters of its name into a Spotlight search. Select it in the results (it should be at the top.)
☞ In the Finder, select Go ▹ Utilities from the menu bar, or press the key combination shift-command-U. The application is in the folder that opens.
☞ Open LaunchPad and start typing the name.
Select All Processes from the View menu, if not already selected, and also select the Network tab.
Click the heading of the Sent Bytes column in the process table to sort the entries by bandwidth usage. You may have to click it twice to get the highest value at the top. What is it, and what is the process? Repeat with the Rcvd Bytes column.
