A father presides over his family. A quorum president presides over a quorum. A Branch President presides over a Branch. A Bishop presides over a Ward. A Stake President presides over a Stake. A Mission President presides over a Mission. An Area President presides over an Area. The President of the Church presides over the entire Church, as directed by Jesus Christ.
Just as a father cannot preside over another man's family, a Bishop cannot preside over a ward other than the one he is called to serve. This pattern holds true throughout Church leadership, although General Authorities have no set geographical boundaries, and they preside at meetings wherever they go in the world.
During a Church meeting, the one who presides is the Priesthood holder in the highest leadership position with stewardship over that meeting. For example, a Bishop would normally preside over his ward's Sacrament Meeting, but his Stake President would preside if visiting for that meeting. However, a Stake President traveling outside his Stake does not preside over Sacrament meetings in other Stakes, because he has no stewardship nor authority over those stakes.
The one who presides over a meeting does not always conduct the meeting (in the sense of announcing speakers, etc.), but he is responsible to assure that correct doctrines are taught and to correct or expound upon false or misleading statements by the speakers. Presiding authorities are to "conduct the meetings as they are led by the Holy Ghost, according to the commandments and revelations of God." (see Doctrine and Covenants 20:45)