A proxy agreement is written authorization for one person to legally act on behalf of an other person. The most common form of proxy agreement grants one person to vote stock on another person's behalf. In most cases, any power a stockholder has to vote at a shareholder meeting can be granted to the proxy.
The most common form of proxy agreement is one where a shareholder assigns their right to vote to another person for votes taken at a corporate shareholder meeting.
Proxy voting is common in legislative voting and the process is outlined in "Riddick's Rules of Parliamentary Procedure." Proxy voting is only allowed when the legislative body had agreed to adopt its use in their proceedings. In this case, the legislator votes in absentia by submitting their vote in writing prior to the actual vote.
At the most basic level, a proxy agreement is simply an agreement for one person to represent another person.