Witch hazel is a smallish tree (up to 5m) that's native to North-America, has nice yellow flowers and is similar to the hazelnut bush (hence the name).
As for skincare, it's loaded with active components that have a bunch of magic properties, like astringent, anti-inflammatory, antioxidant and anti-bacterial. It's also a well-known vasoconstrictor (it makes the blood vessels narrower) and promotes the healing of broken skin by tightening up the skin proteins and thus creating a protective covering.
The complication, however, is that different extracts and distillates can be made from different parts of the plant (bark, twigs, and leaves are typically used) and different extraction methods from different parts produce different results. So if you see only Witch Hazel Extract or Witch Hazel Water on the ingredient list, it's a bit hard to know what you're actually getting but we will try to summarize the possibilities to give an idea.
The main biologically active components in Witch Hazel are hamamelitannin (a potent astringent and antioxidant), catechins (anti-inflammatory and antioxidant) and gallic acid (antibacterial). The bark extract contains by far the most hamamelitannin and it has the most gallic acid and catechins. The twigs contain fewer catechins, less gallic acid, and much less hamamelitannin (4.77% vs 0.18%). The leaves contain hardly any tannins (0.04%) or catechins and contain a medium amount of gallic acid (compared to the bark and twigs).
Witch Hazel also contains tiny amounts of the essential oil and fragrance component eugenol, but the amount is so small that it's probably not significant for the skin.
Apart from the differences in active components in different parts of the Witch Hazel bush, the extraction methods also vary. Witch Hazel Distillate contains 14% added alcohol according to the USP specifications and alcohol is, at best drying, and at worst skin-damaging. Luckily, there are also alcohol-free distillates, so if you prefer no alcohol check the ingredient list carefully. Witch Hazel Extracts can also be made in different ways: browsing Ulprospector, we could find hydroglycolic, hydroalcoholic and glicerine/water based extracts.
Well-known skin care expert, Paula Begoun rates witch hazel as poor and says, "depending on the form of witch hazel, you’re exposing your skin either to a sensitizing amount of alcohol or to tannins, or both." This might be the case if you are dealing with an alcoholic witch hazel bark water or extract, but looking at CosIng (the official INCI name listing of the EU), witch hazel bark water or witch hazel bark extract are not listed ingredients. Bark and leaf or bark and twig or all three are used together to create extracts, so the chance that there is too much hamamelitannin in the final cosmetic ingredient seems small. Also alcohol-free extracts and distillates exist; actually, the majority seem to be alcohol-free nowadays. So all in all, we think "Hamamelis Virginiana Extract" on the ingredient list is nothing to worry about.
We even found a German study that compared the efficacy of Hamamelis ointment to panthenol ointment for soothing the skin in children (from 27 days to 11 years old). They observed 309 children and concluded that both ointments were similarly effective but the one with Hamamelis was even better tolerated (98.2% vs. 92.3% tolerated well the ointments in the two groups).
All in all, Witch Hazel Extract is a sloppy INCI name (btw, not in the CosIng listing), and you do not really know what you're getting. Most probably though, you are getting a goody with nice astringent, soothing, antibacterial, and even antioxidant properties.