Either a pilot or an air traffic controller may use the phrase
stand by. Think of it as aviation speak for "hold on a second" or "I'll be right with you."
When used by a controller, it generally means that he or she must pause in talking to you because there is a more pressing issue demanding attention. Pilots sometimes use the phrase for the same reason but are more likely to use it to ask the controller to wait while they find the information the controller is seeking. For example, if a controller asks a pilot whether or not he can make a significant diversion from his planned route, the pilot may need to make a quick fuel calculation before responding. By asking the controller to stand by, the pilot is letting the controller know that he will respond momentarily. When the pilot is ready, he should radio the controller with the information.
An air traffic controller may also ask a pilot to wait, as in, "Stand by for clearance." It's important to remember that this is neither an approval nor a denial of the requested clearance. Occasionally, controllers forget about a request. If you have not received a response within a few minutes of being asked to stand by, re-establish contact with the controller and, if necessary, remind him or her of your request.