The word actually explains itself: On-street parking means parking your vehicle on the street, anywhere on or along the curb of streets, in contrast to parking it in a parking garage. In some streets you can always park your vehicle on the street, but sometimes there are restrictions. Mostly these restrictions are presented on traffic signs. Sometimes you’re only allowed to park on one side of the street, and sometimes you’re not allowed to park your vehicle at all. There are also on-street parking situations where you need a parking permit to park. To make sure people follow these rules and restrictions, cities hire enforcement officers.
Off-street parking means parking your vehicle anywhere but on the streets. These are usually parking facilities like garages and lots. Off-street parking can be both indoors and outdoors. Off-street parking also includes private lots, garages and driveways.