Configuration bits control the various logic, Flip-Flops, muxes, bus switches of the connectivity mesh, IO options, etc.
The configuration bits are being uploaded after power-up from an external source (like flash memory or microcontroller), such that the FPGA internal elements are configured to implement your design. Depending on the application, the FPGA can be re-configured (rewriting the configuration bits) later during the product operation, to change functionality.
The configuration bits cannot normally be accessed by the user.
About user bits - sound to me like SRAM blocks and other memory bits that can be used in your design (if needed, have to see specific datasheet for more details).