1. Ready for use. E.g. "The graph plotter's fixed and on-line again".
2. Interactive as opposed to batch. Accessible via a computer (or terminal), rather than on paper or other medium.
3. Of a user, actively using a computer system, especially the Internet. E.g "I haven't been on-line for three days."
"On-line" should be hyphenated because it is compounded from two words but the hyphen is often omitted in names of organisations or services.