I am also mystified by these "banks" but I'm even more perplexed by the entire notion of private investment in infrastructure.
When the government builds infrastructure that is an investment because that infrastructure will contribute to higher GDP (increased/improved traffic or information tech leads to increased commerce and higher sales/incomes/business revenues) which results in greater tax revenues. Private industry doesn't tax, however, so for them to build infrastructure as an investment they need to find some other way to extract money. And because most private industry operates on much shorter time scales than the government, they need to do that fast, which generally means much larger rents than the market would support.
Imagine a road if it is funded by tax revenue then it is "free" to drive on, which means any business that wants to start up there has an advantage in that its employees and customers don't need to pay to get to them. That is good, and it means that business is more likely to start there. It may be 5 years before that business turns a profit and pays taxes (though it will likely pay employees which means some payroll/income taxes, but those may just be displaced from elsewhere).
Now imagine that same road funded by a company that wants to profit. Either they are going to make it a toll road or there will be lots of parking fees, or they will charge any business/resident some fee for access points. Any of those things will make starting a business (or building houses, or anything) on that road less desirable than the above, and so the build up would be even slower. Slower buildup means that the company will need to charge more to see any return on its investment and we have a downward spiral.
This is a bad idea in every way imaginable, and yet it is one that is increasingly common as stupid, short sighted, or just rotten politicians try and make a quick buck at the expense of future revenues.