Apple - Can I share iCloud Drive folder with other iCloud user?
Before macOS High Sierra and iOS 10 release the answer was "No - iCloud drive and its folder structure is strictly for sharing with one account." You can now share files but not entire folders easily.
Now with iOS 10 and High Sierra and newer, you can share from the share control on macOS and choose a file. You can share with the generic "add people" icon files but not folders currently. You can share from the web interface and iOS as well.
For some iWork documents and photos, you can share them individually or by adding someone to a shared photo album, but that's based on the app design and not a more general folder based file sharing idiom.
You can also avail yourself of all the share sheets when an app like Things or OneNote or Acorn can accept a shared file from iCloud.
Also - Apple's MailDrop feature to email each file to the recipient(s) that need to share the file, but it wouldn't be anything that's hosted and really shared in the sense that a change to the file by one user would then be reflected on the cloud. When that works it's great since you don't have to plan to share out the files - it just happens.
Clearly, iCloud isn't competing directly with Box.com and DropBox but it has picked up tons of useful features and the live on line collaboration for iWork documents and notes is really fantastic in 2018 now that we have some real sharing features in iCloud.
As it currently stands (March 2015) you cannot share iCloud folder, but you can share individual iCloud files. Even if your recipient does't have iCloud account they will be able to view and edit your iCloud documents.
Open a document on your iCloud site, and click share button on the top toolbar. You will be given a link and some options (readonly vs editing, password protection).
Since September 2017 (iOS 11), you can now share files via Files app (or on iCloud.com).
Simply navigate to the file you want to share -> click on the share icon -> click "Add People" -> then you can share a copy of the link to the file/folder.
For some reason, folders aren't supported yet.