Motherboard Standoff Screws
Motherboard standoff screws are usually coarse threaded screws which allow for the motherboard to be installed/put into the computer's case.
The most common type of standoff is a brass hex-shaped standoff screw and it can be installed using a hex driver tool, although they are usually relatively easy to screw in using your hands. Another type of standoff is one with a clip style that snaps into the case's tray.
Standoff screws are necessary because the motherboard couldn't simply be screwed directly into the computer case (this is because the case is metal, and if the motherboard touched this metal case it would cause a short-circuit and possibly damage some of the computer's components).
Hence standoffs are used to create a buffer between the case and the motherboard, and thus allowing for the motherboard to be inserted into the case in a safe way.
The image below shows the two standoffs described above. The brass standoff screw (left) is fairly common, although the clip-style one (right) is still used - albeit less commonly - today:
Installing Motherboard Standoffs
The brass motherboard standoffs (or the clip-style ones) are screwed into the computer's case in a way that lines up with the motherboard. You can determine where these holes are by looking at the motherboard - it will have holes in particular places (please note that the four holes around the CPU socket are not applicable; these are to install the CPU heatsink/cooler). Using this as a reference, determine where the standoff screws need to be placed in the computer case.
Screw (or clip) the standoffs into the case's tray. Once this is complete, carefully lower the motherboard into the case and insert it through the standoffs, being careful not to touch the case with the motherboard. Once this is complete, use the actual (non-standoff) screws provided to screw the motherboard into the standoffs. Do this gently since you do not want to damage the motherboard.
This is pretty much all that is required to install the motherboard standoffs and hence the motherboard into the computer case.