Tearing is a distracting visual artifact. It typically looks like horizontal lines running up and down the image. Tearing occurs if the display is refreshed while the CPU is in the middle of writing a new frame to the graphics hardware. At that moment, both the old and new frames are partially visible, and if they differ (as is likely), the eye perceives a discontinuity (a tear) in the image.
Tearing can be only prevented by using full screen mode; this allows DirectDraw to synchronize access to the graphics hardware. In normal windowed mode, tearing is unavoidable.