Hide photos means, simply, remove them from this view. They don't go anywhere and you can show them/hide them with an instruction in the View menu. It's handy if you want to show someone a few pics, but just leave these other ones temporarily out of sight.
There are two related but different types of Photostream. Let's assume you have an iPhoto, and iPad and a Mac.
My Photo Stream:
Take a pic with the iPhone and it shows up on the iPad and Mac - if you opt in to the process. (For instance, I don't. It's just not a thing I'm into). Basically it's a way of getting your shots onto every device without having to import them first to the Mac and then to the iPad. There are two key limits on this:
The photo is removed from the Stream after 30 days or 1,000 images - which ever limit comes first. This doc has a lot more detail
http://support.apple.com/kb/ht4486
So, think of it this way: take a snap with the camera and it's available on the other devices for 30 days (or until 999 more have been taken). You have that time to decide to add the photo to your iPad. It can be automatically added to the Mac, as that has more space.
iPhoto Menu -> Preferences -> iCloud
Check the box at Automatic Import
In the case of photos you add to iPhoto on the Mac these can also be streamed to devices under the same terms. So, as you add photos to iPhoto they are streamed to the devices. This might be the one you want to shut off.
iPhoto Menu -> Preferences -> iCloud
Uncheck the box at Automatic Upload
Now, images you add to iPhoto on the Mac will not be pushed automatically to the devices.
Shared Photo Streams
These are a way of selecting images to share with the devices. So, pick the favourite 45 images from your holiday and Click on the Share Button lower right. More on that here:
http://support.apple.com/kb/HT5903