Shatt

Shatt is the slash ship between Shiro and Matt from Voltron: Legendary Defender.

Canon
Matt and Shiro were two out of three crew members to go on the mission to Kerberos. How well they knew each other prior to the mission is still unknown.

After the crew was captured by Galra both Shiro and Matt were sent to the Gladiator arena to fight. Matt was due to go in first but Shiro faked a violent outburst injuring Matt's leg in the process to prevent Matt from being thrown into the arena putting Shiro in his place instead. It worked as Matt was sent away but the two never saw each other again during Shiro's time as a Galra prisoner.

In season 4 the two were reunited after Pidge discovers Matt's whereabouts and brings him back to meet team Voltron. Matt addresses Shiro formerly but Shiro cuts him off to bring him into a hug. From this point on the two address each other like friends/comrades.

Fanon
The ship while small was founded very early in the fandom soon after the release of season 1. Many like the idea of them being good friends from the Garrison but recent canon material may suggest that the two were not acquainted until they were picked for the Kerberos mission. Still, fans like to imagine how they bonded while travelling through space together.

Trivia

 * In early 2017 a voice actor from the cast of the show leaked a scene from the recording booth on one of their social media profiles. In the photo the TV has a shot of Matt and Shiro standing together seeming like they're posing for a fight against a common enemy. This scene has yet to be seen in the show.