A TWAIN driver (see twain.org) is a piece of software that installs onto your Windows PC or Mac and controls your scanner from there. With any modern scanner, there will be a TWAIN driver included in its software package. Once installed, you shouldn't have to think about it again, or even know it's there.
A modern OCR package will usually find your TWAIN driver and use it to control the scanner. This is very handy. There may also be a small scanning package with your TWAIN driver, which will provide a screen where you can make fine adjustments to scanner settings, and start scans. You probably won't need this, since your OCR package will probably do it for you, but it may be useful for semi-manual control of the scanner.
Unix-based systems like Linux use SANE (www.mostang.com/sane) rather than TWAIN drivers.