Fortnite Battle Royale's Solo Showdown is a Limited Time Mode, and is being used as a "one-off stepping stone to learn how to build great events for all types of players". This mode is very clearly aimed at Fortnite Battle Royale's best and most-skilled players (such as record-setting players like Ninja) and Epic also teases a "major announcement about competitive play" coming next week.
It's the game's first try at a competitive mode which uses self-selection instead of the usual matchmaking.
Even if you're not lucky enough to rank in the top 100 players of Fortnite's Solo Showdown mode, by simply playing 50 games, you'll get a unique spray, so there's always that. Epic Games hasn't confirmed anything about this so far which means that we'll have to wait in order to find out whether or not Fortnite is actually getting a competitive mode. The developer is introducing a new Limited Time Mode they're calling Solo Showdown.
Epic will want to know if Solo Showdown makes lower skilled players feel left out, makes them feel as though they want to get much better at the game, and so on. There doesn't seem to be an in-game Solo Showdown leaderboard, though Epic will update the standings on its blog post.
"In the Solo Showdown LTM you will be placed against other self-selected competitors making this the ultimate test of survival". Once the limited time mode ends, the top 100 players will receive a prize. It's just that you're being tracked for the first 50 matches you play within Solo Showdown to see where you stand. At the end of those 50 matches, a score will be given.