A company will be eager to expand into, say, a Third World market, if they see a way of increasing the profits of the company. They want to do this very much, in an excited, gleeful, even ecstatic 'dollar-signs in their eyes' kind of way - there's money to be made!
Pepsi-Cola may be anxious to expand into a Third World market that Coca-Cola has already started up in, because Pepsi also want to expand their company; but are worried that if they delay, Coca-Cola will have firmly established itself and have market dominance there. Hence, they want to do it very much, but are also worried about the competition and being too late and left behind. They are anxious to start production and distribution there as quickly as they can: they are keen/eager, but also worried about the competition. In this way, 'anxious' expresses both ideas.
Similarly, a foreign country may be giving huge tax incentives for overseas companies to invest there, but these benefits will cease after a certain period of time. Hence, a company will be anxious to expand by starting a business in that country: they are keen and eager, but they need to do it quickly because they have the worry of having to get a business up and running before the deadline and the tax incentives no longer are in their favour: They are anxious to expand there while the economic situation is favourable to them.