The word designated has several meanings, depending on its context. Generally speaking, it means to assign a particular role or function to someone or something. In other words, it refers to selecting someone or something for a specific purpose. For example, you might say that the team's captain is the designated leader, meaning they are in charge of leading the group.
In addition, "designated" can also refer to an area set aside for a particular use. For instance, there may be a designated smoking area within a building or park where people can smoke without disturbing others. In this sense, it means reserved or allocated for a specific purpose.
Finally, the word can also imply that something is officially recognized or approved. For example, you might say that someone has been designated as an official representative of their country at an international meeting, meaning they have been given authority to act on behalf of their government.