Developing countries ( and democracies at that), need private sector investments. At least in India the private sector is no substitute for the govt and hence investments are routed through the public private partnerships (route). It is win-win for both the parties: The govt gets kudos for getting the infrastructure asset up (theoretically the govt does nothing in the partnership except for facilitating the ease of construction, i.e. ensure that this project is safe from other other arms of the govt.) and the developer gets the benefit of an asset class that would provide steady cash flows to him.
Is it profitable?
Sure is, the most important thing in India is to get the asset up, which can be way beyond the project schedule.
The demand has always been there, more latent than pronounced in some cases (think power the peak deficit is only 10,000 MW but most of the country is in darkness)
Since the licenses are for periods of 25-30 yrs, the asset and surrounding areas bring in monopoly rents
What are the dynamics:
Revenue share: The do all end all, the govt would set up a base price, the bidder would bid at a particular amount of the base price + a revenue share. Revenue share is nothing but the money you are paying to the govt. for letting you put up the asset at the expense of state resources. Thsi determines who wins the bid at the end of the day.
Traffic: Irrespective of whether the asset is a port, road or an airport the most important thing is to guess (yes guess is the operating word, no one really knows what the potential of anything in India is, its a way too complex combination of cost benefits, so they surmise - but there are enough tools to guess right more often than not) the traffic that the asset will support. The difference is revenue share bid out by different companies relies primarily on this difference in estimation of traffic. You believe that the traffic will be so high that with the costs (most costs are pretty much fixed whether for x traffic or 3x traffic), giving the developer huge cash flows.
What can go wrong?
As I wrote before, a lot can go wrong, but primarily greed and the government's need for control: More often than not, the developer will bid an obscene revenue share and then realize that his cost structure does not support the bid that he has put in. Hence creative ways to fleece the end consumer. Typically the corruption benefit of an asset approved under one govt. will accrue to the next govt (construction time of 3-5 yrs), so the govt. have really no incentive to keep a tight leash on the bidding process (thing navasheva sewri link). If everything goes right, then both sides want to make money as soon as possible and end up pushing the project out too fast (the international airport in hyd seems like that case), leading to operational chaos.
Still, given all these kudos to the promoters who have the balls to try and put out these assets tying up crucial cash for years together in the hope of some mirage. Only the unique animal called the Indian Promoter can attempt it.
PS: I have created a file with basic numbers for understanding the concept.