From the County Commissioners Handbook:
All Ohio counties organized under the general statutory law have three county commissioners, two being elected at the time of the presidential election and one at the time of the gubernatorial election. The county commissioner elected at the gubernatorial election takes office on January 1st, and the two elected at the presidential election take office on January 2nd and 3rd. Candidates for these two commissioner positions must file for either the January 2 or 3 position (ORC 305.01).
County commissioners make up the general administrative body for county government. As indicated above, they can perform those duties which are specifically authorized by the General Assembly and no more. They are the county government taxing, budgeting, appropriating, and purchasing authority. They hold title to county property. Individual commissioners have no power to act independently. All formal and official actions must be taken by the board of county commissioners acting as a body by majority or unanimous vote.
Commissioners also have a myriad of other responsibilities including hearing and ruling on annexations, approving drainage improvements through the petition ditch process, establishing water and sewer districts and making improvements, and providing for solid waste disposal.
Commissioners also appoint department heads of offices for which they have responsibility and also appoint members to a variety of boards and commissions, and also serve on some boards such as the board of revision, the county records commission, and the planning commission.