The FPGA can load its configuration from a flash chip. The FPGA itself cannot store anything non-volatile. You must use it on a board and configure it each time the power comes on. Up until now you have been doing this with a JTAG cable (I assume).
You can also program the EPCS16 serial flash device on the DE2 board. According to the user manual, page 24, this can be programmed over JTAG by assigning a POF file to the device in the chain. Then the FPGA will configure from that flash device each power up.