Most of us know balloons from festivals and fun fairs, where they are colorful and amusing, but in the 19th century, before airplanes were invented, balloons were used in wartimes to spy on the enemy position. One or two men would go up with a telescope in a balloon tied to the ground with a rope. However, because the enemy might fire a cannon at them, this was dangerous.

So before men would go up in a balloon, they would first float (or send up) a trial balloon without any men in it to test the situation. If the enemy tried to shoot that trial balloon, the men would not go up. From this origin, today we use this idiom in any situation where we want to measure public reaction or opinion before committing a lot of money and effort to some project.