Coins is the currency of Anno 1800. They are required to construct almost all buildings and buy goods, ships and items. You can also use them to send gifts to computer players to increase your reputation or pay for various diplomatic agreements.
They can be obtained by fulfilling needs of your population, trading with other human or computer players, selling ships to neutral traders, holding shares of other players' islands and completing quests from computer players. Occasionally you can also get a gift from other computer players.
Your balance reflects how many coins you gain or lose per minute. It includes income from residents, maintenance costs of buildings, upkeep costs of ships, shares value, tourists income and royal taxes.
A lion share of a Player's regular income consists of fulfilling your population's needs. See the page on the Profitability of Consumer Goods for a summation of the most profitable options.
You can go bankrupt if your money amount goes down to -5000 . At this point you might still get a second chance as Archibald Blake can give you 25000 for free. However, after reaching -5000 again you will go bankrupt. Bankruptcy means losing the game, it should be avoided at all cost.