BITNET means "Because It's Time Network".
It was composed only of educational institutions, although the protocols it ran were used for a huge network internal to IBM, which was larger than other networks such as ARPANet for quite a while. Bitnet links originally ran at 9600 baud. The software that ran Bitnet was eventually ported to non IBM mainframe OSes.
Bitnet featured e-mail and listservs, but predated network services such as web sites, FTP or Gopher. You could also send short messages to other users (a feature exploited by Bitnet Relay Chat), as well as files.
One joke about Bitnet was that it stood for "Because Idiots Type Network".