BIAB stands for “Builder in a Bottle” — originally a brand name, now used generically the way Kleenex is. It refers to a thicker, self-levelling builder gel applied over the natural nail as a strengthening overlay: more structure than gel polish, less bulk than acrylic. Cured under a lamp, it adds genuine flex-resistance, which is why it has become the go-to system for growing out bitten, peeling or post-damage nails — the nail lengthens under protection.
A BIAB set typically wears three to four weeks and can often be infilled at appointments rather than fully soaked off each time, meaning less acetone and less filing over a year. If your nails “just won't grow” (they grow; they break), BIAB is very likely the answer a good tech will suggest.