It is easier to think about this in reverse - i.e. what does it mean for light to be approaching from infinity? When we reference light from an object at infinity, we mean that the object is so far away that all light rays (strictly speaking in terms of geometric optics) from the object appear as if they are parallel and traveling in the same direction. When these parallel rays approach the convex lens, they get focused to the focal point of the lens.
In optics, the direction of light travel does not matter, thus when an object is placed at the focal point of the lens, the light rays will become such that they are perfectly parallel and traveling in the same direction. This is usually called "collimated" light.
This method of collimating a light source (or object) is generally used in various imaging techniques such as shadowgraph and Schlieren.
Now what will happen if you place your hand in the optical path of the light? Well, theoretically, you should see nothing since no image is formed from parallel light. But in reality the light will never be perfectly collimated so you may see a very blurry version of whatever your object is. As soon as you place another focusing element in its path though, all those light rays will be focused at its focal point and you will (theoretically) have a perfectly formed image of your object.