Around the horn in baseball is act of the infielders (usually just the catcher and the basemen) throwing the baseball to each other with the purpose of keeping their arms loose and warm between plays where there is little activity like a batter being struck out.
What happens when there are no base runners at all? Sometimes, if the batter is put out and there are no base runners, the infielders will throw the baseball to each other in order to keep their arms loose and warm between inactive plays.
If the batter struck out, the players will begin throwing around the horn with the catcher, who usually throws it to the third baseman, who will throw it to another infielder, and it will continue for each infielder until the baseball is returned to the pitcher. If the runner was thrown out at first base, the throwing will begin with the first baseman in a similar fashion. This is only done when there are less than two outs; once the third out has been made, all the fielders will simply run back to the dugout.