If I am developing a web service for retrieving some album names of certain artist using an API, and I am asked:

The service should give the possibility to paginate results. It should support 'ofset=' and 'limit='.The default limit is 50 and you can increase that up to 150.

How should I interpret that? I get confused with the meaning of "ofset" and "limit"

Paginating means you do not get all results, but pages with up to limit results.

limit  == how many results to return per call  
offset ==  which "page" you are on if limit == 50 and offset == 150 you return results 151 to 200 (page 4)

You should use a default limit of 50 results and return 150 results per page at maximum even if a limit of 1000 is requested.