The blue floppy disks in the store say they increase server health. I think it operates much like the fuses, in that it acts as a buffer for the server going down. If you give a server health with the blue floppy, in the event that it would go down, instead it drains the health by one and stays functional. It seems like it's the new "server protection" mechanic, only it's based on giving them a buffer instead of just rendering them immune to breaking for a set period of time.
...Though, I haven't tested this myself, so I could be wrong. That's just how I interpret what the game is telling us. An easy way to test would be to feed a server (preferably not upgraded so it breaks sooner) a blue floppy, install the Global Alert module, and see if it ever tells you that the server is merely "damaged" instead of "down".