On Kindle Fires and Kindle Fire HD you need memory for a lot of stuff and this is a tutorial on how to clear space without losing your files forever.
Step 1: Connect the Kindle to a Computer or Laptop
To do so, take the USB off the charger. Then plug one end to your computer/laptop and one end to your Kindle. I'm guessing you can figure out which end goes where yourself.
Step 2: Transfer Files You Don't Want
To do this, go to the files you don't want and drag them across to the "My Pictures" folder so you will still have a copy.
Step 3: Delete the Files You Don't Want
Now, just delete the files from the device (not "My Pictures" folder this time) and you are done!