To help you have a semi-fundamental understanding:
Your computer, whether it's a laptop/desktop or Mac/Pc, is comprised of hardware- parts like the screen, the processor, the graphics card, the RAM, the power supply, the motherboard, the hard drive, the fans, the keyboard and mouse, the webcam, and whatever else you might plug into it.
Now, think of something which you use your computer for on a daily basis: Playing games, using the internet browser to post on Yahoo answers, etc. This is software which you use. However, your hardware also requires software too. The software which is required by your hardware is called the "device drivers" essentially because they are what drive that device to "work".
Lets say you plug in a webcam into your computer. How does your computer know that you just plugged in a webcam? Or a keyboard? There is a device driver software which provides the computer with information about the thing which you just plugged in, and gives your computer directions on how it works and lets you use it.
Often, when you have an "outdated" driver, it can cause something which your computer relies on to stop working properly. So essentially updating your drivers can help fix compatibility issues and other hardware issues which you might be having.
The operating system is in charge of using these device drivers and handling the input/ and output as well as other tasks such as providing you the ability to use the computer and delivering the user experience. As well as memory management, the multitasking of processes to be run on your CPU and all sorts of other cool stuff.
Hope that gives you some insight.