There is a list of about 80 games for the Xbox 360 that can be played on the Xbox One through a form of backwards compatibility. More games are being added to this list on a semi-regular basis -- often as part of a pre-order bonus of some sort. For example, the entire Gears of War series was made backwards-compatible upon the release of the remastered version.
This works best for titles you own digital copies of, and going forward most games for `360 offered in the "Games with Gold" program should be backwards compatible (according to Microsoft), so you'll gradually build up a library of titles if you remember to claim them on either your `360 console or the web.
Titles you own digitally that are eligible should appear in the "Ready to Install" portion of the "My Games and Apps" app when signed into the same Xbox Live account.
The backwards compatibility also works for disc-based games if you have any that are on the list, but the disc simply acts as a licence for the content -- you'll need to download the emulated version from Xbox Live before you can play it.
Because the compatibility is done through software emulation, rather than the console natively being backwards compatible (as was the case with the PS1->PS2 compatibility) there are occasionally minor performance issues in the emulated version that don't exist in the original game. These are in my experience fairly rare though.