The chips or "little black rectangles" as they're technically referred to are called ICs which stands for
Integrated Circuit and basically, they can do anything. There are literally thousands if not hundreds of thousands of different ICs out there. Some are standard and very common, others are custom built for a very specific need or purpose. To ask what the chips do without anymore information is like asking, "What does a machine do". If you want more information of the specific ICs in your picture then your best best it to read the part numbers off the top of them and do a search on the interwebs. The other non-IC components are likely resistors, capacitors, diodes, transistors, etc. If you can take a better picture of the circuit board without the wires obstructing all the components, I might be able to help you identify what type some of the other components are.