A Transport Subsidy or Subsidy is an incentive for you to transport a designated type of cargo from one specific location to another. The Local Authority will usually notify all players about the subsidy through the Newspaper. Any subsidies available, or any subsidies you or other companies in the game have been awarded (either AI or player-controlled) will appear on this screen:
A subsidy is awarded the first company that provides the designated service within the subsidy expiration date.
The Local Authority will increase the amount of revenue made by delivering the designated cargo type between the two locations mentioned in the subsidy in the next year, which can range from two up to four times the original revenue.
Players that take advantage of subsidies can find themselves making more money than players who do not. Subsidies are a good way for new players who join a multiplayer game to get a strong foothold easily.
Up until the 0.7 branch (inclusive), the following rule applied for being awarded a subsidy: If you are carrying cargo to a city, your station (that is the station 'flag'), needs to be within 9 tiles of the city center (that is the town 'flag'). The same holds for industries, your station 'flag' needs to be within 9 tiles of the 'industry' flag.
As of r17113 (first stable release with these changes will probably be 0.8.0), the above rule was removed and changed to the following: Any house belonging to the town (in case of a town being the subsidy destination) or any tile of the industry (in case of an industry being the subsidy destination) need to be in the catchment area of the station you are delivering to, in order to obtain the subsidy.
Another change introduced in r17113 is that awarded subsidies are no longer bound to a specific station. This means you can earn the extra payment in all stations in/near the target town/industry, instead of only in the one the subsidy was awarded for.