Mineral oil is a mixture of liquid hydrocarbons left after petroleum is refined, then purified until nothing aromatic or reactive remains. On skin it does two things. As an occlusive it forms a thin film that slows water evaporating out of the outer layer — a reduction usually put at around 20 to 30%, less than petrolatum's 98% but enough to matter, and far more comfortable to spread. As an emollient it slips between the flat surface cells and fills the gaps, which is why skin feels smooth immediately after applying it.
Its molecules are too large to pass through healthy skin, so it stays where you put it. That is also why it is the standard base for eye ointments: if a little reaches the eye surface it causes a few minutes of blurring and nothing else. Its other useful trick is dissolving oily material. It loosens thick greasy scale on the scalp, cradle cap on a baby, and sunscreen and makeup on the face, which is why it appears in cleansing oils.
Cosmetic-grade mineral oil is very well tolerated, and like petrolatum it is used as a negative control in allergy patch testing.
Do not swallow it, and do not give it by mouth to a child, to an older adult with swallowing difficulties, or to anyone at risk of inhaling it. Breathing it into the lungs causes lipoid pneumonia, which is why liquid paraffin is no longer used casually as a laxative. Do not use it inside the nose regularly, for the same reason.
Do not use it on an open wound, a fresh burn, or infected skin — a plain sterile ointment is the right choice there.
If you are acne-prone, keep it off the oily areas of the face. It does not cause acne, but it is unnecessary weight on skin that does not need it.
Everyone else is fine, including in pregnancy, while breastfeeding, and on babies. If you object to petroleum-derived ingredients on other grounds, that is a values decision rather than a safety one — but be aware that plant oils cause allergic reactions more often, not less.
Immediately. Skin feels smoother the moment it is on, because the oil is filling the gaps between surface cells.
10 to 15 minutes, for scale. On the scalp, one soak softens thick scale enough for it to wash away. This is the fastest thing it does and the one most worth knowing about.
Within a day. Dryness and tightness ease if you are applying it to damp skin and repeating it.
Two to four weeks. Regular use keeps rough, dry skin comfortable. Cradle cap usually clears within a few weeks with oil and gentle washing — though it also tends to clear on its own regardless.
When you stop. Within days. Mineral oil manages dryness rather than changing the skin, so the effect ends with the last application.