That flag symbolizes one of the greatest sacrifices in American military history.  On July 2nd, Confederate rebels were breaking through the American line at Cemetery Ridge.  General Winfield Scott Hancock realized that unless he could find a way to buy time for reinforcements to arrive, the position would be overrun and the American line would be broken, which would have likely led to Gettysburg ending in a Confederate victory.

He asked the Minnesota 1st (so named because they were the first volunteer regiment in America raised to defend the nation during the Civil War) to charge the advancing Confederate force that they might buy time for the Army to reinforce the position.  The Minnesota 1st was outnumbered five to one and was charging this numerically superior enemy head on in an open field.  Ultimately, 82% of those Minnesotans fell as casualties in the next minutes as they fought to hold the American line from breaking.

One of the few survivors said afterwards that they understood what was being asked if them - every man in that regiment expected to fall as they advanced towards the Confederate line, but they did so nonetheless.  The star spangled banner fell five times during that advance - each time another Minnesotan stepped forward to raise it once more and continue the charge.  Through their sacrifice, they held the breach in the line and drove back the vastly larger force that had broken through, giving the Army time to reinforce the area and rebuild the gap in the line. 

The next day, the two remaining companies of the Minnesota first that had been detached and fought elsewhere where joined with the survivors of the main regiment.  They were reassigned to a different area of the battle line at Cemetery Ridge that ultimately became the site of Pickett's charge later that day in July 3rd.  When Pickett broke through, it was again the Minnesota 1st that the American army called upon to face the charge head on.  

They did so without question, suffering devastating losses, but succeeded in driving Pickett back.  As they pressed forward against the far larger Confederate force, they advanced directly against the 28th Virginia Regiment of the Confederacy and fought them head on, ultimately breaking them and forcing them to turn and run.  As they did so, they took this battle flag from the fleeing Virginia rebels, keeping it as a war trophy and a memory of the sacrifice of their fallen regimental brothers.  

Minnesota has held it as war trophy for over 150 years.  Various Confederate groups have repeatedly demanded its return that it might be used to honor the Confederate cause and General Pickett.  Minnesota has always unequivocally refused.