A WG or Wohngemeinschaft is an apartment where multiple people live together and share the rent. It’s called a shared apartment or flatshare in English. Living in a WG is a good way to save on rent. Most WGs are listed on WG-Gesucht and Kleinanzeigen. For more details, see this guide.
A Zweck-WG is a WG where people live together to save money, not to be friends.