Caffeine
In plain terms
The same caffeine as in coffee, used in eye and body creams as an antioxidant that temporarily tightens and de-puffs skin. On the skin it is well-tolerated and low-risk; the de-puffing is real but short-lived, and the cellulite claims are modest at best.
What the evidence shows
In skincare, caffeine works as an antioxidant and a mild vasoconstrictor, which is why it shows up in eye creams for puffiness and dark circles and in firming or slimming creams. It penetrates skin readily, and at the concentrations used (up to about 3%) it is considered highly safe, with clinical studies on caffeine creams reporting good tolerance and no significant adverse effects. The visible effects are modest and temporary: tightening and de-puffing that fade, and small, mixed results for cellulite that owe a lot to massage. As an antioxidant it may add some defense against UV-related damage. This is the same caffeine found in coffee and tea, so there is nothing exotic to worry about on the skin; taken in food and drink it is a well-studied stimulant rather than a contaminant, with moderation (and lower intake in pregnancy) the only real consideration. On the skin, it is a low-risk, gentle active whose main limit is how much it delivers.
On the label
Listed as caffeine. Useful for a quick, temporary de-puff around the eyes; keep expectations realistic for cellulite. There is no skin-safety reason to avoid it.