Imagine a random walker dropped somewhere on a graph, taking one random step at a time. How long before its position becomes unpredictable?
That time is the mixing time.
A low one means the walk reaches a stable, spread-out distribution quickly: every node is reachable soon regardless of the starting point. This shows a well-connected graph.
A high mixing time means the walk stays trapped near its start for a long time, or stuck in a loop.