CubieBoard is an ARM board.
System on a chip: Allwinner A10
CPU: 1Ghz ARM Cortex A8
Can I put Debian on my CubieBoard?
Yes, but currently (Apr 2013) CubieBoard is not officially supported by Debian.
Unofficial images are available, e.g. Cubian (see links section)
Cubieboard manufacturer website
Debian image build and installation guide from the Sunxi wiki
Cubieboard main page on the Sunxi wiki