Oil-based lubricant covers a whole range of products including commercial products such as Elbow Grease, Slam Dunk, and Butter Boy (designed for anal use), Yes, 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 toys, and fisting.
Oil based lubricants are not compatible with latex condom. They will degrade the latex causing the condom to break.
More About Oil-Based Lubricant
There is some debate as to the safety of using oil based lubricants in the vagina. Generally, as the thick oil based products do not wash away they can become a breeding ground for bacteria, making them a poor choice for partners with vaginas. However, coconut oil may be an exception to this rule as its antimicrobial properties seem to out weigh the risks. Coconu lubricant uses coconut oil as its base.
Products like Slam Dunk, Elbow Grease, and Boy Butter should never be used in the vagina but are excellent for anal play and hand jobs.