The so-called "
Taiwan Guoyu" is the standard
mandarin of Taiwan. It is the counterpart to the mainland's "
putonghua", both of which are basically standards for mandarin pronunciation. The main differences between the two is that Taiwan guoyu uses less rhotacization of finals (a fancy term that basically means "that 'er' sound that people from northern China add to the end of their words) than does putonghua.
Also, there are many examples of different terms between Taiwan and the mainland, like how Americans say "truck" where British say "lorry"
Alternately, people commonly use this term to refer to someone who speaks the mandarin language with a Taiwanese accent, pronouncing "sh" initial sounds as "s" . An example, the pronunciation of "shi" (4th tone) ("to be") changes to "si" (the number four).
Actually this change of the sh initial's pronunciation is common throughout south China, with some people from areas as far apart as Guangzhou, Taiwan and Shanghai all changing these sounds, this difference in Mandarin accent between northerners and southerners is a good quick way to tell where someone is from.