Please note that I am not recommending this, I just read about it, and wanted to give it a try, and I was asked for a little more info on what it is.. but I can’t see any reason that it would be harmful, and so it fell in line for me as a “why not”
Here is the idea-
The practitioner rinses their mouth with approximately one tablespoon of oil (sesame and coconut oil are the most recommended) for 15–20 minutes on an empty stomach (before eating/drinking) then spits it out.
This process makes oil thoroughly mixed with saliva. As the process continues, the oil gets thinner and white. The oil is put in the mouth, with chin tilted up, and slowly swished, sucked, chomped and pulled through the teeth. The oil changes from yellow and oily consistency to a thick viscous consistency. One must ensure that the oil is spit out before the purported toxins get re-absorbed by the body. If the oil viscosity starts thinning while swishing, it should be a sign that toxins are getting re-absorbed. A second round of oil pulling may be done with fresh oil for further cleansing. The oral cavity is then thoroughly rinsed and washed with normal tap water and fingers or tooth brush. This procedure is typically performed daily.
There is some scientific literature on the use of oil pulling therapy, like one study that reports on the effect of oil pulling therapy with sesame oil on the oral health status. In this study there was a definitive reduction in the S. mutans count in plaque and saliva after oil pulling therapy. The mechanism by which oil pulling therapy causes plaque inhibition and reduction in S. mutans is not known. The viscosity of the oil could probably inhibit bacterial adhesion and plaque coaggregation. Other possible mechanism might be the saponification or the ‘soap-making’ process that occurs as a result of alkali hydrolysis of fat.  Sesame oil is a vegetable fat and when acted upon by salivary alkalis like bicarbonate, the soap making process is initiated. Soaps are good cleansing agents because they are effective emulsifiers. Emulsification is the process by which insoluble fats like sesame oil can be broken down into minute droplets and dispersed in water. Emulsification greatly enhances the surface area of the oil, thereby increasing its cleansing action.  But more studies have to be done to prove the antibacterial effect of the components of the sesame oil. Cited from Asokan S. Rathan J. Muthu MS. Rathna PV. Emmadi P. Raghuraman. Chamundeswari.