What are sprays?

A spray is a graffiti-like tag that you can place onto the environment for other players to see.

The default keybinding is T, or D-Pad Up on console.

Screenshot via reddit:

Sprays are icons that you can tag on walls and such. Some are unique to each hero, while others can be used by any hero. The icon that will be tagged can be selected from the owned tags available to that hero. According to this reddit you apply sprays by pushing "T", and it seems you have to be relatively close to a wall to use it.