Today I'm going to discuss the difference between essential oil and regular oil, and how they both relate to henna. First let me clear up some confusion. Essential oils and regular oils (such as coconut oil or olive oil) are completely different. The term "essential oil" is really a misnomer. Essential oils are chemically more similar to an alcohol and are a plant essence (usually steam distilled, but sometimes pressed). A regular vegetable oil, such as coconut oil, olive oil, or mustard oil (a staple in some Indian kitchens), is thicker and may have a greasy consistency.
Some essential oils have properties which can increase the staining potential of henna. This is why some people apply "nilgiri" (eucalyptus) oil to the skin before a design is applied. Most reputable henna artists add the essential oil (such as tea tree, cajeput, cardamom, or lavender) to the actual henna mixture, making this pre-application unnecessary. You can read about how to use essential oils in your henna paste here.
Further adding to the confusion is the fact that some henna-for-hair recipes call for vegetable oil. This is for conditioning the hair and does not help the stain. In fact it can inhibit the staining properties somewhat.
A thick vegetable based oil can be applied after the henna paste has been removed. Real vegetable oils (not their distilled counterparts) protect the skin from water, and nourish the skin so that it doesn't take on an ashy appearance.
Here we can see henna made with essential oil, and once the paste has been removed it is protected with coconut oil. Both parts of the process resulted in a rich dark stain 24 hours later.