Latinum is a rare liquid that cannot be replicated, which makes it the most widely accepted currency in the Alpha Quadrant when suspended in gold as gold-pressed latinum.
Because replicators can produce most objects on demand, a currency must be something they cannot make. Latinum fits the need, but it is a liquid, so for trade it is suspended in worthless gold to form gold-pressed latinum.
Gold-pressed latinum circulates in units of increasing value, the slip, the strip, the bar and the brick. The Ferengi, whose culture revolves around profit, measure success in it, and Quark spent years scheming to earn more.
The Federation's own economy no longer runs on money, but Starfleet officers and Federation citizens deal in latinum when they trade with other powers, and it figures in many dealings on Deep Space Nine.