A proxy firm (also a proxy advisor, proxy adviser, proxy voting agency, vote service provider or shareholder voting research provider or proxy voting advisory businesses (PVABs)) provides services to shareholders (in most cases an institutional investor of some type) to vote their shares at shareholder meetings of, usually, listed companies.
The typical services provided include agenda translation, provision of vote management software, voting policy development, company research, and vote administration including vote execution. According to their websites, not all firms provide voting recommendations and those that do may simply execute client voting instructions.
The votes executed are called "Proxy Votes" because the shareholder usually does not attend the meeting and instead sends instructions - a proxy appointment - for a third party, usually the chairman of the meeting to vote shares in accordance with the instructions given on the voting card.