A band is one part of the color gradient (continuum) that is more than one pixel wide and of the same color. This means that if an application requests RGB(200,200,200), it could be getting the same thing from RGB(201,201,201). If these bands are quite wide (15 pixels or more), they could have a realistically noticeable effect on image reproduction if you have acute vision and view the area of banding up close.
Here I have a couple programs to test it (The GRADient LINearity test):
For Red, Green, Blue, Gray colors:
http://xtknight.atothosting.com/tools/gradlin-v0.2.exe
For Red, Green, Blue, Gray colors (fullscreen; press ESC to exit):
http://xtknight.atothosting.com/tools/gradlin-v0.2-fs.exe
For Cyan, Magenta, Yellow, Gray colors:
http://xtknight.atothosting.com/tools/gradlin-cmy-v0.3.exe
For Cyan, Magenta, Yellow, Gray colors (fullscreen; press ESC to exit):
http://xtknight.atothosting.com/tools/gradlin-cmy-v0.3-fs.exe
If you see vertical conglomerates of colors, then that is banding. At least from my experience, lots of LCDs have bands of 5-10 pixels but if it's wider your LCD may be entering the sub-par territory.