Petroleum jelly forms a barrier against moisture.
Thus, when applied to something dry that generates moisture/etc, it will trap said moisture.
Human skin generates moisture. That includes your lips and... other parts.
Consequently, one might be able to posit that applying vaseline, that is to say petroleum jelly, would perhaps form a barrier against the moisture of our skin.
This barrier would be between the skin and the air, with the moisture being trapped under it.
If the moisture can't escape to the air, it would simply stay put, resting under the barrier.
This would make the skin moist.
If the skin is moist, it isn't dry.
Thus, petroleum jelly can aid in keeping skin moist, and preventing it getting dry, provided your skin can indeed generate moisture, which it most certainly does unless you have some odd condition that prevents you from generating any moisture whatsoever, in which case it would not help form a barrier against moisture, instead forming other kinds of barriers (for example, against bacteria or other airborne particles/etc.)
This is all just my hypothesis, however. I'm not a dermatologist.
Also, in my own personal experience, do not trust anyone who has anything related to "Holism" in their description.
If you're seeking genuine medical advice about something, think to yourself about whether you would want whoever is giving you medical care to brand themselves the way your source of advice does.