Observation holes tend to look spherical in shape and most are old and worn out as if they were hundreds of years old and have never been maintained.
Observation holes are a necessity for Shinigami. The observation holes make it possible for Shinigami to find human victims without going into the human world. If a Shinigami already knows the name, lifespan, and face of a human, they can use the observation holes to instantly locate and watch the human by thinking of what they look like.
These holes can be found all around the Shinigami Realm; there are even "desert areas with holes for looking down to earth. Nothing else is necessary." 
Despite the importance of these holes, it is unknown when they were created.
Throughout the plot, the observation holes are used very rarely. The Shinigami Gelus uses it to watch a human girl he has grown attracted to. It is also used later on by Sidoh in an attempt to locate his lost Death Note.