The queen is the most important bee in hive its true but other bee's also have the same value in the hive. No ones importance is more or less in the hive. Worker bee's doing the maximum duties in the hive. Like collecting the nectar from outside, Pollen, water etc. They also work for indoor duties like making hive and repair them. Nursing duty, cleaning work, security work feeding to queen, fanning in summer, heating the hive in the winter.
The queen and the worker bee's are the same female but there are a little difference between both. Queen is only one in the colony and the workers are in thousands. The reason to producing queen bee is the bee's fed the larva by Royal Jelly which is the reason to make queen with the same larva. But worker bee's can feed the royal jelly to the larva to produced new queen.
1.) If suddenly there is no Queen in the colony
The worker bee's find the absence of the queen bee in the colony to feed royal jelly to the larva is the main reason for introducing the new queen in the colony. Some times by any reason the queen is missing from the colony without any reason may be she died accidentally or any other reason. Mainly queen bee comes out of hive only during the meting time. This is the reason of the How to decide which larvae of honey bees should be fed with royal jelly to become a queen?
2.) If Queen is died for any reason
Some times queen bee died in the hive and suddenly there will be no queen found by worker bee's. Queen can lay eggs daily up to 1500 to 2000 eggs daily. When she will die there is also some eggs available in the hives. When worker found no queen in the hive they going to make a new queen by feeding some eggs by royal jelly.
3.) Eggs must be needed to make queen
The workers make the queen only when the eggs in the hive available. If there is no eggs then its too difficult to produce the queen. They noticed very early when queen is missing from the colony. Then they soon going to start the feeding to the larva by royal jelly.
4.) Larva is not mature when the feeding royal jelly
When the worker bee's decide to feed the larva by Royal Jelly they choose less aged larva. Too old larva is not much useful to produce a good queen. They create more then one queen cell because sometime the queen cell is fail to make queen or can be damaged by any reason. That's why they make more then one queen cell in the hive.
Conclusion
The queen is the mother of the colony its very important to growth of the bee colony to produce the eggs in the hive. If queen is not in the colony the colony doe's not live long and die in two to three month. If you are a bee keeper you will need to re queen the colony.