Lobbying is a major component of the game. Once cities reach certain sizes, they will start proposing laws that may affect your business (they will). Laws are highly localized and depending on their location and nature may only impact your company to a limited degree. Whenever you want to mess with democracy, you can use lobbyists available once the Lobbying Department is added to the office.
Lobbyists will attempt to influence the vote in the target city. The earlier they are dispatched and the more of them there are, the higher the likelihood they will succeed. Most laws have a limited timeframe and expire after a time (usually 180 or 365 days), but certain charges, such as a 70% tax on mail, can severely undercut companies that rely on those commodities for their bottom line.
Indirectly, this is also a good way to wage economic war on your rivals: If they rely on certain goods and you don't, lobbyists can help cut into their profits and drive them out of business - or at least give you some breathing space.