What triggers puberty?

Still largely unknow. We still do not know precisely, yet certain hormonal chemicals are well know to play a major role such as leptin, gpr54, kisspeptin and melatonin.
Genetics leptin. Genetics is one factor. Achieving a certain body weight, especially body fat. Adipose makes leptin, which is a signal to the brain to start making reproductive hormones. Girls with low body weight (eg gymnasts, balarinas) often have a delayed puberty.