Birthstone.
A gemstone associated with the month of one's birth, drawn from a list with both ancient and modern (jewellery-trade) versions.
A birthstone is a gemstone linked to the month a person was born in. The custom is old and layered. Early sources connected the twelve stones of the breastplate of the high priest in the Book of Exodus first to the twelve tribes of Israel, then (by writers such as Josephus and St Jerome) to the twelve signs of the zodiac, and only later to the twelve months of the year. The month-by-month version most westerners know today was formalised in 1912 by what was then the American National Association of Jewelers, with later additions and substitutions to suit the trade.
The standard modern list runs: garnet for January, amethyst for February, aquamarine for March, diamond for April, emerald for May, pearl or moonstone for June, ruby for July, peridot for August, sapphire for September, opal or tourmaline for October, citrine or topaz for November, and turquoise or tanzanite for December. Some traditions retain alternatives, and zodiac birthstones (assigned by sign rather than month) overlap but do not match exactly.
Birthstones make easy gifts because the link is personal without being presumptuous. They also give beginners a natural place to start a small collection.