The first and last line of defense against the titans, the military that almost the entire cast of Shingeki no Kyojin is a part of is divided into three distinct branches, each one with an unique role and methodology. The differences between the military branches are symbolized by the emblems that distinguish them, all relying on the power of icons to display to the people what their purpose is and what they do to stand against the titans. But what do these logos stand for, and how do they paint a clearer picture of the world of Shingeki no Kyojin as a whole?
The Training Corps
Before taking a look at the three branches, it's important to first take the emblem of the Training Corps into account. Being the source of fresh recruits for the entire military, it's without a doubt the foundation of humanity's defense, and this is reflected by their emblem. The crossed swords, two offensive weapons locked in a defensive posture, capture the heart of the military, regardless of branch. An organization prepared to give as good as they get and all trained toward one common purpose: opposing the titans.
The Garrison is the largest of the three branches. They're always the first to deal with the fallout of titan breaches, and so they suffer the highest casualties out of any branch as they frantically try to cover the civilians' escape.
It's only fitting that their emblem is two roses, then. In Christianity, the red roses are a symbol of the blood of martyrs, which would be an apt description of the Garrison's role, dying for the sake of the innocent.
The Military Police
The elite of the elite, if only in status and not ability. Choosing the unicorn as their symbol makes it pretty clear what type of organization it is: something almost unobtainable for most of the populace. Only the most privileged are allowed among their ranks, and if they do join they'll inevitably get involved in a world of rampant corruption as they milk the cushiest job behind the walls.
The Survey Corps
The branch that the main cast is a part of, and always on the front lines. They're the only group actively seeking to recover humanity's lost glory, and this shows in their emblem. Referred to as the Wings of Liberty, this, along with the frequent dove imagery in the second opening, represents their desire to break free from their confinement behind the walls, representing Shingeki no Kyojin's central theme of emancipation.