1. [adj]  (computer sci) connected to a computer network or accessible by computer; "an on-line database"
2. [adj]  (transportation) on a regular route of a railroad or bus or airline system; "on-line industries"

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.