This is a phrase used in baseball to describe runs scored by a team after they have secured the lead. This applies to any amount of runs and can be used during any segment of the game. The concept is that adding more runs on top of the lead provides a buffer between the two teams. How late in the game a team is able to score insurance runs contributes to how the team gaining the "insurance" are able to take advantage. Late game insurance runs are usually considered more valuable than insurance runs scored early.
If a close game is only broken by a team scoring one run, it is a significantly easier for the other team to come back and tie the game again. If the game is close but then one team scores lots of runs, the other team will have a lot harder time catching back up, especially if the runs are scored late in the game. However, if lots of runs are scored early in the game, the team could take advantage by subbing in players who need game experience. This would only be done if the manager felt assured of a victory.