The phrase has been floated by democrats recently, with no description of what it is. Presumably an infrastructure bank would loan money to cities and states for infrastructure projects. Roads, high speed rail, bridges, broadband, Big Dig style tunnels, maybe even electric power plants. It would get the money to loan by selling bonds on Wall St. It would be a "government sponsored entity" (GSE) like Fannie and Freddy are. As such, investors would be willing to buy its bonds cheaply because the full faith and credit of the United States stands behind them. That's how Fannie and Freddy worked. Infrastucture Bank could borrow at 3 and a skosh percent, much lower than cities and states can borrow, and loan out at 4 or 5 percent, still better than cities and states can do.
Infrastructure Bank would have a large, well paid, staff with full benefits, and members of Congress get to hand out these plum jobs to friends, relatives, and supporters. Always a good thing for incumbents.
Infrastructure Bank borrowing would not show up in the Federal deficit. It could borrow as much as it liked and not make the official deficit worse. At least not until it went broke like Fannie and Freddy did a couple of years ago. Then all of Infrastructure Bank's debts become US taxpayer debts.
Infrastructure Bank gets to say which (or whose) infrastructure projects get funded. Projects for friends and supporters get loans. Projects in political enemy's districts don't.
All in all, it's a way to run up the public debt, hand out cushy jobs to the well connected, and centralize control of infrastructure spending in Washington.
What's not to like?