These terms were used in my data structures textbook, but the explanation was very terse and unclear. I think it has something to do with how much knowledge the algorithm has a
An on-line algorithm is one that receives a sequence of requests and performs an immediate action in response to each request.
In contrast,an off-line algorithm performs action after all the requests are taken.
This paper by Richard Karp gives more insight on on-line,off-line algorithms.