Scanlines are the visual appearance of the electron stream passing over the phosphor of a monitor. Where the electrons hit the phosphor, they glow and create the image on the screen. The "scanline effect" is an attempt to recreate the feel of the otherwise low number of lines of an actual arcade monitor on the much higher resolution screen of a computer or LCD.
Visually they appear as the alternating bands of image and darkness. They create a subtle softening and blending of the otherwise hard-edged pixels. It is a purely personal aesthetic choice how to deal with this.
Here is an image from my 29" VGA monitor:

This is somewhere in-between a classic arcade monitor and a computer monitor.
This is a K7400 25" arcade monitor.

Notice that the little RGB cells are not in a perfectly aligned grid? This means that the classic scan 'line' is not actually a hard edged line. It's somewhere in between. Even this close you'll be hard pressed to identify a single 'pixel' because of this staggering of the phosphor.