Long run in poker refers to an extended period of time or a large number of hands / tournaments played. In live poker, these two things usually come together, but in online poker, it is possible to accomplish the long run in a relatively short period of time.
For example, 100,000 hands played by a cash game player constitute a long run, and 1,000 tournaments played also qualify.
This is an expression that you’ll often hear from experienced grinders who understand the game. Your results in poker are only relevant if you look at them over the long run. After playing enough hands or tournaments, you can figure out your expected win rate with a good degree of certainty.