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Monitors and printers work in different ways and can reproduce a different set of colours, neither of them can reproduce the complete set of colours that the eye can see. The set of colours that a monitor can produce is often represented by a colour wheel
The white box represents colours that the eye can see but the monitor can't show.
Monitors blend light ( rgb or red [C], green [A], and blue [E]) to produce a relatively large range of colours.
Printers work by mixing inks absorbing light (cmyk or cyan [F], magenta [D] and yellow [B] ) and produce a much reduced range of colours indicated by the triangle. They also add a true black ink (the k in cmyk) as cyan, magenta and yellow mixed only produce a dirty brown.
Some (expensive) modern ink jet printers add red and blue inks which helps and sometines even a grey.
But it will never solve the problem completely.
Printing shops produce plates for each colour, apply the ink to the plate and roll the plate over the paper. To get a specific colour (e.g. for a logo) they will add a 5th or 6th plate with additional colours which can't be reproduced by the cmyk process, these are called called spot colours and can easily be distinguised from normal colours as they are used in blocks rather than applied as dots. Black logos on the back of DVD covers are often like this, when scanned you can see a sharp edge not a blurring of dots.
Compare the white and red text on this cover and the background blue.
Scanned at 600dpi - no descreening
The background blue is the general dotty make up of cmyk
The white text is merely the absence of colour which means the edges of the letters are not clearly defined as it depends upon where the dots whould have gone
The red text is a spot colout and the edges are much more defined
From the same cover
The black spot colour makes the gentle curves of the D symbol much more clearly defined than it would have been otherwise
This of course hase an effect on scanning prints. If you want to extract the spot colours do NOT descreen, if you do it will look out of focus.