What does the NYSE opening or closing number mean?

usually, any open or close statment in a stock realted conversaion, will refer to the standing of that specific stock. it easily understood when thought of in company security( stocks) i.e. say google opens ( 10am) at a stock price of 40$ a share, and closes(4;30pm) at $45, that would be the open and close prices for google on that given day.