As for "hide" as mentioned in the help, I can only assume that by hide they mean to remove it from focus -- possibly by scrolling far enough in the document where it can't be seen -- but is still selected and manipulatable. I don't know of anyway to, in literal English, hide a persistent selection.
The easiest way to explain it . . . would be this, I hope -- you're accustomed to non-persistent blocks. By blocks, I mean a "block" of select text. In non-persistent blocks, moving the cursor unselects text. Entering a keystroke will overwrite the text (delete it) altogether.
With persistent blocks, however, this behavior changes -- the blocks of selected text literally persist. When you move the cursor, the block of text will remain selected/highlighted unless you select/highlight another block of text. Further more, keystrokes will apply normally where the cusor is, without interupting, unselecting or overwriting the selection. Pressing ctrl+delete is the means, generally, for deleting a persistent block.
For me, personally, the benefits of persistent blocks are--
* moving the cursor to look around at other parts of the body of text will -not- cause your selection to be lost
* hitting a key will not accidentally delete the text
* Select now, use later. Some times I know what I want to select, but am not sure what I want to do with it precisely -- and if I simply cut it to the clipboard, there's a good chance I'll forget about it
* In editors that support it (EditPadPro for example), you can select a block, move your cursor to a different location and duplicate or move that block of text to the cursor's location. Normally this would require more steps -- copy/cut, find location, paste as opposed to simply hitting ctrl+d or ctrl+m to duplicate/move the block.
It's a somewhat subtle difference, but one I find myself unable to live without these days
Abridged, bottom-line version: Persistent selections are not unselected or overwritten by a keystroke like normal selections. Instead, they remain until you move, delete or unselect them (by selecting something else).