I've been watching some replays on Day9 TV (which I highly recommend for any players looking for indepth explanations of strategies) and I noticed he has replays saved in folders within "Multiplayer". It's quite easy to create a folder, but I can't figure out how to save a replay to that folder, or to move a saved replay into a new folder. Amazingly, Google hasn't shed much like on this. So, how do I save replays into a folder, or move saved replays?
In your "recent" replays folder in game, there is a button to the left called "Keep". Pressing this button will move the replay into the "Multiplayer" tab if it was a ladder or custom game.
Then, from here, navigate to your SC2 account directory, which on Windows is usually located under:
C:\Users\Username\Documents\StarCraft II\Accounts\Some Numbers Here\Some More Numbers Here\Replays\Multiplayer
Also, you can download replays from the internet and then copy them directly to that folder, and they should show up instantly under the "Multiplayer" replay tab in the game!
In addition, any of the replays that you have not selected to "Keep" should show up under the "Unsaved" folder within your account under "Replays", here:
C:\Users\Username\Documents\StarCraft II\Accounts\Some Numbers Here\Some More Numbers Here\Replays\Unsaved
That folder will only keep about 25 of the most recent replays before it starts replacing the old ones, so please refer to this question for more options on how to save more, or manage your replay saves.