Ask your developers! It's not possible to hide the fact that you are non-technical, so you might as well gain some points for trying to learn about their field. They might even have some books lying around that you can borrow.
A concrete book that I would recommend to everyone in software project management is Rapid development by Steve McConnell. It is a really good book both for general project management, and especially about the software construction process, however it won't go into details of explaining what API's and databases are.