Astaxanthin is a carotenoid, i.e. a carotene-like chemical.  Carotenoids, and especially astaxanthin, protect cells against oxidation by 1) quenching singlet oxygen and dissipating the energy as heat and 2) scavenging free radicals to prevent and terminate chain reactions. Due to its particular molecular structure, astaxanthin serves as an extremely powerful antioxidant. It has a very effective quenching effect against singlet oxygen, a powerful scavenging ability for lipid and free radicals and effectively breaks peroxide chain reactions Carotenoids are effective at low oxygen concentrations, complementing the activity of vitamin E which is effective at higher oxygen concentrations.  Natural astaxanthin has been shown to be a potent antioxidant over 500 times stronger than vitamin E and 10 times stronger than beta-carotene. Astaxanthin has also been shown to enhance and modulate the immune system. These effects in combination or separately may reduce the acute inflammation reaction of the skin and tissue just beneath the skin that follows excessive exposure to UV radiation.

Seki, Taisuke; Sueki, Hirohiko; Kohno, Hiromi; Suganuma, Kaoru; Yamashita, Eiji (2001) Effects of astaxanthin from Haematococcus pluvialis on human skin. Patch testing, skin repeated application test, effect on wrinkle reduction Fragrance Journal : 29(12), 98-103.

Savoure, Nicole; Briand, Gilberte; Amory-Touz, Marie-Christine; Combre, Alain; Maudet, Maryvonne; Nicol, Marc (1995) Vitamin A status and metabolism of cutaneous polyamines in the hairless mouse after UV irradiation: action of beta-carotene and astaxanthin. International Journal for Vitamin and Nutrition Research: 65(2), 79-86.

http://en.wikipedia.org/wiki/Astaxanthin