FPGA's are a special kind of digital microchips. Unlike most other microchips they do not come with a predefined function, but the user (the engineer who is designing some kind of electronic device) can design a function for the chip by designing a circuit for it on a computer. Then the design can be programmed into the FPGA. If the design does not do what one wants, it's easy to change it on the computer and change the way the chip works.
FPGA's contain hundreds (or thousands) of CLB's. One CLB is a rectangular area on the chip that contains a lookup table, a flipflop and Routing. A Lookuptable allows you to create a logic function (AND, OR, XOR). The Flipflop allows you to make that function synchronous (based on a clock signal). And the routing is just a lot of "wires" that can connect your CLB to some other CLB.