A device driver is a small piece of software that tells the operating system and other software how to communicate with a piece of hardware.
For example, printer drivers tell the operating system, and by extension the program in which you have opened the document you want to print, exactly how to print the information on the page.
Sound card drivers are necessary so that your operating system knows exactly how to convert the ones and zeros in an MP3 file into audio signals that the sound card can send to your headphones or speakers.
The same general idea applies to video cards, keyboards, monitors, mice, disk drives, and so on.