The title is a colloquial term for the British East India Company, the organisation that ran British India (and their own army) in the 18th century. In the game, players represent families whose members work for John Company. Between them, the players build up the Company while competing for preferment.
Depending on the scenario, the game lasts a certain number of rounds – unless brought to a premature end by something disastrous like the Indian Mutiny. Players gain points for the shares and prizes they've accumulated and the most points wins.
The game is full of historical detail that makes it a real experience to play. There's also a solitaire game which is a very useful way of learning the rules – though there are a lot of these, many will only matter in very specific circumstances. This is top of my list to play as soon as I can.
For 1-6 players, aged 14+, playing time 2-3 hours: £36.00 (£30.00 tax free outside the EU)