As many have said, it usually is in reference to a certain level of important bacteria in the nitrogen cycle; however, I think the term is also often used when describing a tank that's been running with stable parameters for a long time (i.e. ~years). One way to think about it is the longer a tank goes with stable, healthy parameters, the more "mature" it is. Mature tanks are generally more resistant to problems, as inputs (light, food, fish, etc.) are in a stable balance with chemical processes and outputs (biological filtration, plants, water changes, algae control, etc.).