This summary is as good as any other:
The first big new feature in WPA3 is protection against offline, password-guessing attacks. This is where an attacker captures data from your Wi-Fi stream, brings it back to a private computer, and guesses passwords over and over again until they find a match. With WPA3, attackers are only supposed to be able to make a single guess against that offline data before it becomes useless; they'll instead have to interact with the live Wi-Fi device every time they want to make a guess. (And that's harder since they need to be physically present, and devices can be set up to protect against repeat guesses.)
WPA3's other major addition, as highlighted by the Alliance, is forward secrecy. This is a privacy feature that prevents older data from being compromised by a later attack. So if an attacker captures an encrypted Wi-Fi transmission, then cracks the password, they still won't be able to read the older data -- they'd only be able to see new information currently flowing over the network.
Note that we're just getting the new standard this week. Actual devices that implement the standard are still months away.