Yes if your internet provider wanted to lookup what you're browsing and what websites you're viewing or what files you're downloading then yes they can easily lookup your history through there software.
So if you do something illegal such as looking up child porn or download illegal things such as illegal movies etc then if the police caught onto what you're doing and then wanted to prosecute you for that then the police can contact the ISP and summon them to lookup your browsing history and hand it over to them so they can use it against you.
Usually though the ISP is not interested in actually what you're browsing or downloading and don't sit there and look at what you're looking up or what sites you're on.
It would take too many employees to just sit there and watch what everyone is doing on the internet and is not economically feasible.