Here's a simplified description:
A driver is a piece of program code that provides the specific support
for a piece of hardware.
I'll use the example of a printer driver. There are many thousands of
different printers manufactured, by different companies, and each of
these printers needs to be communicated with using the specific code
it was designed for. If all of these thousands of different pieces of
code were incorporated within Windows, Windows would be many times
bigger than it is now, and would also constantly be going out of date
as new printers hit the market.
So that's not what happens. Windows doesn't talk directly to the
printer but to a little piece of software sitting between Windows and
the printer itself. That piece of software is called a "driver." Each
printer manufacturer writes a driver for Windows when he releases the
printer, and each user of that printer has to install that driver. So
you have the driver installed for your printer, brand A, model X, and
I have the driver installed for my printer, brand B, model Y. The
interface between Windows and the driver is the same, but the
interface between the driver and the printer is different for each
printer.
But it's slightly more complicated than that. I said that the
interface between Windows and the driver stays the same, but that's
only for one version of Windows. If you change the version of Windows,
you need a driver capable of talking to that new version of Windows.
So each piece of hardware needs several drivers, one for each version
of Windows it can work with.
Generally when a new version of Windows comes out, the hardware
manufacturers write new drivers to make their devices work with it.
But if you have an old printer (or any hardware device), when a new
version of Windows comes out, the Manufacturer may not bother writing
a new driver because so few people still use it. Conversely, if you
have very new hardware, the manufacturer may not have yet written a
driver for it to be used with the latest version of Windows.
A piece of hardware without a driver for your operating system is
useless.