Photoshop uses your computer's RAM to store information about the image you're currently working on. If Photoshop runs out of available RAM, it uses your hard drive space to store this information - the so-called "scratch disk".
One solution would be to install more RAM, although the best solution of all is to install a second physical hard drive and use that just as a scratch disk, but I realise that not everyone can run to that. Otherwise, it's a case of freeing up some space on your existing HDD. The general rule is that you should have approximately three to four times the amount of hard drive space than the file size of the image that you are working on.
This is the "official" answer, from the Adobe knowledge base:
Error "Scratch Disk is Full" When Editing a File in Photoshop - Support Knowledgebase