Ergodicity is a mathematical property describing whether patterns found by comparing many different people (between-person data) also hold true for a single person changing over time (within-person data).
It sounds abstract, but the implication is concrete and a little unsettling for personality science: most trait research is nomothetic — it looks at how people differ from each other across a population — and then quietly assumes those between-person patterns also describe how any one person functions across time. That assumption is called ergodicity, and it usually doesn't hold. Knowing that Conscientiousness correlates with life satisfaction across a large sample doesn't guarantee that your Conscientiousness and your satisfaction rise and fall together week to week. The relationship that shows up when you compare thousands of people isn't automatically the relationship that governs one person's inner life.
Psychologist Peter Molenaar's 2004 paper on this problem is the key reference point in personality science; he argued that psychology had been treating non-ergodic processes as if they were ergodic for decades, largely because group-level statistics are so much easier to collect and analyze than genuine within-person data gathered repeatedly over time.
This is part of why idiographic methods and intensive individual tracking have gained ground in recent years — they're one of the few ways to actually check whether a nomothetic finding applies to the person sitting in front of you.