It depends on the context. If you mean it in a context similar to "a bird flew overhead" or "overhead luggage" it simply means above head-level. In a business setting, overhead refers to indirect costs which are incurred by the operation of the business.
"Move Overhead" is the assumed delay, in milliseconds, due to network overhead/lag. Setting a higher value for your chess program can help avoid clock flags, especially if you don't have great internet connection.
Of course, there are many other definitions of "Move Overhead", such as the one @clousems provided :)