Coumarins are good anti-inflammatories, and they reduce both oedema and redness on our skin. They are anti-bacterial and may offer anti-fungal activity. Some studies have shown promise using coumarins to treat Candida albicans, although "more study needs to be done" (in other words, they're not sure).
Coumarins are an interesting addition to sunscreens. They block out the short wave radiation (280 to 315 nm) but allow the longer wave radiation that allows us to get a nice tan.
But coumarin has a dark side. It is suggested we don't ingest more than 0.1 mg per kilogram of body weight due to possible liver damage. It's not known if coumarin applied to the skin can enter the blood stream, but just to be safe the EU requires labelling for any product containing more than 10 ppm (leave on) and 100 ppm (rinse off). And it has been banned as a food additive in most countries - it happened in 1978 in the US. Why? Because is is a powerful anti-coagulant - it's the drug Warfarin - and it can be used as a rodent killer by making the poor animals bleed out and fail to process Vitamin K.
This doesn't mean we should avoid coumarins in our diet or our products. Coumarins are found in coconut oil, lavender, liquorice, Tonka beans (hence the vanilla scent), apricot, cherries, strawberries, and cinnamon. They offer anti-fungal, anti-inflammatory, and anti-oxidizing properties. They can reduce water retention and reddening of the skin, and may protect from UV damage.