It's just barely possible to fit an extremely minimal Linux system on a floppy. (Here are a few examples; beware that many of these span several floppies.) With just 1.44MB, there is no have any room for any application; I think you can get a minimalistic command line with no interesting command to run.
As an example of a more realistic tiny system, my home router runs Linux. The whole disk image (kernel plus programs) fits in 4MB (in fact, I think it's close to 2.8MB). That's a dedicated system, with an old kernel version, only the drivers needed for that particular device, and not many programs — mostly networking administration tools, including a small web server, an SSH client and server, a shell.
A distribution like Ubuntu or Fedora comes with thousands of programs. Some of these programs take tens of MB on their own. Some of these programs' documentation takes tens of MB. Just the device drivers for all the peripherals, network protocols and other parts of the kernel take about 100MB these days — there are so many different devices one can connect to a PC.
For a basic system with a GUI and a web browser, you'll need a couple of hundred MB. For a more complete system with a full desktop environment, a word processor and so on, count on a couple of GB. If you start having multiple alternatives for each program (Gnome and KDE, Firefox and Chrome, …), the sky's the limit.
If you feel like comparing with the size of Windows, keep in mind that a Linux distribution contains much more than the equivalent of Windows: distributions like Ubuntu and Fedora ship a lot of applications that you would need to install separately on Windows.