Hexylresorcinol slows down tyrosinase, the enzyme your pigment cells use to build melanin. Less enzyme activity means less new pigment while the pigment already sitting in your skin fades on its own schedule. That is the same target hydroquinone, kojic acid and arbutin aim at, and it is the most common way a brightening ingredient works.
It does a second thing that matters more than it sounds. Hexylresorcinol is a decent antioxidant and it damps down inflammation, and inflammation is itself a pigment trigger. That is useful for the kind of discoloration that follows acne, ingrown hairs or a rash, where the mark is the aftermath of irritation. Calming the skin and slowing the enzyme at the same time is a sensible combination.
On the name. Hexylresorcinol has a six-carbon tail attached to a resorcinol core, and that tail changes its behavior completely. Plain resorcinol is a known irritant and a sensitizer, used in peels and in older acne and psoriasis preparations. Hexylresorcinol has been used for decades in throat lozenges and food processing and does not behave the same way on skin at cosmetic levels. Products containing it are not "resorcinol products." A high-purity grade also contains essentially no free resorcinol.
Hexylresorcinol is well tolerated at the levels used in skincare. Most people notice nothing at all.
There is no group with a hard reason to avoid hexylresorcinol. It has a long history of use in food and in throat products, and at 0.5% to 1% on skin it has a mild profile.
Do not use it on broken, weeping or freshly lasered skin. Wait until the barrier is intact.
If you have reacted to a resorcinol-containing hair dye or peel in the past, that is not the same molecule, but it is a reasonable reason to patch test behind the ear for a few days before putting it on your face.
Pregnancy and breastfeeding: there is no specific safety data on topical hexylresorcinol in pregnancy, which is true of almost every cosmetic brightener. It is not a known risk, and it is not a studied one. Azelaic acid and vitamin C are the two brighteners with the most reassurance behind them in pregnancy, so most clinicians point there instead.
If your discoloration is melasma, understand what you are buying before you start. Hexylresorcinol is a reasonable maintenance ingredient. It is not going to clear moderate melasma on its own.