1. To change to a different suit or to no-trumps if an opponent doubles your contract for penalties.
2. To run a suit is to play it card after card without losing the lead. For example, if dummy has ♣A-K-Q-J-7-5, declarer is likely to ‘run’ the clubs.
3. To take a finesse by leading an honour and play low if a higher honour does not cover it.
For example:
Here you might lead the queen from dummy (North) and ‘run’ it, thereby retaining the lead in dummy for a further finesse.