"Busy as a bee" is an idiomatic expression that refers to someone who is deeply engaged in the completion of a task or set of tasks, making use of all his or her resources to bring about the desired end. Typically, a person who is engaged to this degree has neither the time nor the ability to step away and take on some other task until at least some of the current efforts are completed. This status of being very busy is normally looked upon as a positive sign that an individual is being productive and that results are either already appearing or will be shortly.
The image behind being busy as a bee has to do with the industry exhibited by different types of bees. The honeybee is constantly engaged in tasks that benefit the hive, rarely stopping to rest until a task is done. This same level of industry is often considered admirable in people, especially those who will benefit most directly from the efforts of the individual who is so engaged.
For example, an employer will likely be very impressed by any employee who stays busy, providing that all that activity actually produces some sort of results. The administrative assistant who works diligently and at the end of a business day has managed all inbound and outbound correspondence, taken care of the filing, and completed all the tasks assigned for that day can be considered a truly busy bee. At the same time, an employee who spends more time creating the perception of being busy, but who has little to show for his or her efforts at the end of the day, will not likely be valued so highly, and may shortly be freed to seek employment opportunities elsewhere.
Since being busy as a bee is normally considered a positive attribute, many people strive to make use of their time in the most efficient means possible. This has sometimes led to the development of unreasonable expectations that create a great deal of stress and eventually undermine the success of all or most of the tasks that are undertaken. With this in mind, it is important for people to remember that they can stay busy without taking on too many tasks at one time, instead focusing on no more than is within their ability and working diligently on those projects until they are completed.