Modders and mod users alike have been eagerly awaiting the arrival of a version of Skyrim Script Extender that is compatible with Skyrim Special Edition. That day still hasn't arrived, though after some delays and news that SKSE64 wasn't even being worked on, there's still some good news here. An alpha has appeared, and while it's only intended for mod authors to check out and begin testing, it's still a good sign that someday a full version might be available for everyone.
The Script Extender is a mod other Skyrim mods rely on, as it expands Skyrim's scripting capabilities and allows for added complexity and functionality. A number of mods for the original Skyrim have not been ported over to the Special Edition yet, simply because the same level of functionality isn't available without the SKSE.
So, yay! Good news, it's being worked on. Just to say this again, however: this is an alpha build for mod authors to take a look at. If you're a mod user, don't expect support or questions to be answered by the team working on the new SKSE. Just be patient and keep your fingers crossed that we'll see a complete and working version of the SKSE64 sometime in the future.
If you do want to take a look at the alpha, there's a link within this Reddit post pointing you at the download link, and SKSE's somewhat minimalist site is here.