The Xbox 360 is a console made by Microsoft in 2005. What started off as a console with HD versions of PS2/Xbox games became a success thanks to the idea of Achievements that most non-Nintendo systems used since and Halo 3. Currently it is Microsoft's most successful console that they ever released. The console was known for having reliability issues such as the Red Ring of Death on early models though.
Xenia can run many 360 games including Forza however progress has really slowed down. It is your only option for 360 emulation.