Basically, its a radio. But in contrast to traditional gear, SDRs do not demodulate the radio signal using electronic circuits, but send the received signal to a digital signal processing device (e.g. a PC). This device then takes care of demodulating the signal and maybe doing some other stuff with it (remove noise, render some fancy waterfall graphics and so on).
There are some shiny kits out there featuring SDR capabilities. However, I am a developer. I do not like using stuff which is already done where I could learn something new.
That is why I decided to build something on my own, using an Xilinx Spartan3E FPGA (and the matching development board, because, seriously, soldering an FPGA is no fun at all), a Linear Technology ADC, a bunch of other parts and my bare clumsy hands.