Adding more strings gives the guitar more range (i.e., more notes).
Generally, each string is tuned to a different note, tuned from low to high, so adding a string on either side will give the guitar player access to more notes (generally lower notes). 6-string guitars in standard tuning go down to an E, 7-string guitars go down to the B below that, and 8-string guitars go down to the F# below that, adding 5 or 10 new notes (and they all go up to the same highest note assuming the same number of frets).
There are some oddities – for example, a 12-string guitar just pairs up each of the standard 6-strings; the lowest 4 up an octave, and the highest 2 in unison. It technically increases the range because the octave G string is higher than the high E string, but it’s generally used to make the standard range sound fuller.
There are other ways to increase the range of a guitar by using alternate tunings, but that may involve tuning the strings to a wider interval, which can make it impossible to reach every note in a given position, requiring either unusual stretches or changing position.
Of course, adding strings changes the feel of the guitar since the neck becomes wider. Some players might prefer the size of a 6-string neck and aren’t interested in extended range guitars. As well, having more strings means there are more strings for the musician to mute, which can complicate some basic chords.
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