Sometimes referred to as a standoff and spacer, standouts are small metal or plastic screws that attaches to a computer case and holds the motherboard to the case. The picture helps give an example of a standout. In this picture, the left standout has a screw inserted in the hole to help demonstrate how it works. The motherboard would be placed between the standout and the screw.
Standouts also help keep a motherboard from touching the computer case. If the motherboard, specifically the solder points or other metal pieces touches the metal computer case, it can cause a short to occur in the motherboard. A short can cause the computer to not start up or it can cause damage to the motherboard. Using standouts is critical to prevent shorts from occurring and preventing damage to the motherboard.
Inserting a standout
First, screw the standout into your computer chassis. Once all standouts are in place lay the motherboard on the standouts, and then insert the screw through the motherboard screw hole into the standout to hold it in place.
Most computer cases have several holes for the standout for different motherboard form factors. Make sure you're only inserting standouts that coincide with the holes on your motherboard.
When putting standoffs in the case screw them in tightly, but not too tight to cause the threading to be stripped. By securing them tightly, it can help prevent the standoff from unscrewing when trying to remove a motherboard screw from the standoff.
Motherboard mounting screw hole
In the second picture to the right, is an example of what a screw hole aka mounting hole would look like on the corner of a motherboard. Each motherboard has several holes to help hold the motherboard securely in place. Often the screw holes can be easily identified because they'll have metal surrounding each hole. Some earlier motherboards may also have holes without metal surrounding the hole. For these types of holes, the motherboard should have included a cardboard or paper washer to place between the screws and motherboard.