I understand that when a man in the Church is called to serve in a bishopric he is ordained as a high priest. As a result, the high priest group in my ward consists of many members of past bishoprics. However, there are others in the group that I know have not been in a bishopric.
My question is what are the other factors or circumstances that determine how brethren in the church become high priests? Is it an age/maturity thing (like the other offices of the priesthood)? Or is it that there is a need for someone to officiate in a certain position?
The office of bishop is an office of the Aaronic Priesthood. The bishop is the president of the Aaronic priesthood in his Ward, assisted by his two counselors. However, in order to preside over all the members of the Ward he is also ordained a High Priest. Thus, the bishop is the presiding High Priest in the Ward.
The office of High Priest is to preside over the spiritual affairs in the Church. So, any person called to be a member of the Stake Presidency or the Stake High Council is first ordained a High Priest. The Stake President is the president of the High Priests Quorum in the Stake. In organized stakes today, high priest groups are normally organized in each ward. These are presided over by a group leader and two assistants.
Normally, high priests are either serving as presiding officers or have served in the past as members of a bishopric, a high council or a stake presidency. However, there are circumstances where a member may be ordained a high priest without having a calling to preside. This is not a general practice but is occasionally done so that the member may associate in the priesthood with others in his social group.