is not, as the name might suggest, an oily residue
that is produced by or from babies. It is, quite simply, mineral oil
with a little bit of scent
added to it. It is marketed towards using it for babies, but, as we will see, it has many other uses.
Mineral oil, in an unrefined form, is essentially a waste product from the distillation of gasoline from oil. It consists of long alkanes, with a length of the carbon chain of about 20. This is quite different from a vegetable oil like sunflower oil, which is a triglyceride. This is important from a biological point of view: while your body can digest most vegetable oils, it cannot do so with mineral oil. The latter works as a laxative by lubricating the colon. The advantage is that it does not spoil or become rancid, unlike vegetable oil.
Baby oil can be used to massage your baby with. There are many websites and books on why baby massage is a Good Thing. Essentially, it is said to strengthen the bond with the baby, which makes the baby happier and aids digestion. It is noted, however, that unrefined mineral oil is a carcinogen, and that is is slightly harmful when ingested. It traps moisture in the skin by forming an oily film. This prevents dehydration, but I suppose it would also inhibit temperature regulation by sweating. Unlike emulsions, it does not contain water.
An alternative use is that of shaving lubricant. It has the advantage of being dirt cheap compared to other lubricants (well, it IS a byproduct of the oil industry, after all). It will make your hair softer and reduce the possibility of cuts. It is quite greasy, however.
Baby oil may also help in making them. It can be used as a sexual lubricant. When used as such, it has the advantage of not promoting the growth of yeast and other unwelcome guests. Warning: it weakens the latex of condoms, which may lead to other unwelcome guests or another person to apply it to. Whether or not it is better than water-based alternatives is something I leave to your experimental observations.
In summary, baby oil is nothing more than an oil byproduct, scented, and cleverly marketed towards babies, or rather, their parents. While it is a bit similar to vegetable oil, it is quite different chemically and biologically.