I think this has its main roots in Vietnam when the troops were villified for fighting a war that was considered by many to be immoral.

So supporting means not getting on a person's case for doing their job. Understanding that the troops live in a democratic society that has put them in a situation that they personally may not particularly like. Even if you do not support the overall purpose of the conflict, understand their position.

Others of course will say it is a Republican ploy to support our current conflicts in other lands. If you support the innocent doing their jobs (read troops in this case) in the conflict, then the conflict becomes more palatable. Support of troops = support of conflict. Not a very well thought out slogan imo if it is taken this way.