NaN stands for Not a Number. In most cases, if you see one in a map's level data, an object will be broken. Sometimes it'll just disappear, other times it will do something really wacky and unintended.
NaN's are often unintended by the creator of a map and can result from incorrect characters being used in the level data. They are found as a component of an object's code. Objects with NaN's may be outside of the play area and difficult to remove. Sometimes, objects with NaN's cause an object to produce an effect that was not intended for that object. For example, a thwump may have an NaN that causes it to be motionless and "zap" in a direction that does not match its graphic.
NaN's are generally viewed as a negative or harmful to a map's design. If you make a map and you see that something strange happened to your creation, this is the most likely cause of it.
However, if you NaN a zap/laser/chaingun drone, it won't move. It's a well-known technique used by many mapmakers to increase the efficiency of enemies.