The exploit allows hackers to remotely execute code.
Tech Crunch explains:
In what amounts to an innocuous but important proof-of-concept, a hacker called qwertyoruiopz has released a pseduo-jailbreak that allows you to run arbitrary code on the Nintendo Switch. The interesting thing? Because of a bug in the browser software used on the Switch, the same jailbreak that let iOS 9 users modify their phones has been repurposed to attack the console.
The jailbreak code is available here and it primarily consists of a web server that sends over some code that will let you “overwrite anything in memory.” It doesn’t not actually jailbreak the Switch in any traditional way but instead it shows what is possible.