The phrase has three meanings. The first is the straightforward one of "make someone need to stand-up". The garrison couldn't just keep on sleeping, they had to get out of bed and respond to the battle. The second is also fairly physical and means to stand up because you are enjoying an artistic performance so much. "the encore brought the entire audience to its feet". They are probably clapping and cheering. The final one is the metaphorical version of these. A letter from the company chairman might bring the sales to department to their feet because they had been slacking and need to respond, or because it was so inspiring they felt like cheering. After all of that, I would guess that this passage is using the first of these meanings. The garrison had to get out of bed and return to active duty.