Oil-based lubricant covers a whole range of products including commercial products such as Elbow Grease, Slam Dunk, Wicked Creme (designed for penile use), and Butter Boy (designed for anal use), and Coconu (marketed for vaginal use). It also refers to things that aren't marketed as lubricants at all but sometimes get used for that purpose such as coconut oil, Vaseline, and Crisco.
Oil based lubricants are thicker and more viscous than their water based and silicone counterparts and are often preferred for anal play, used with large sex toys, and fisting.
Oil based lubricants are not compatible with latex condoms. They will degrade the latex causing the condom to break.