Although the percentage varies by culture, in Western countries 85 to 90 percent of people are right-handed and 10 to 15 percent of people are left-handed. Mixed-handedness (preferring different hands for different tasks) and ambidextrousness (the ability to perform tasks equally well with either hand) are uncommon."
Source : US National Library of Medicine - link below
Current theory suggests that multiple genes contribute to the development of handedness - but studies with twins have shown that only around 25% of handedness is hereditary.
There are various theories regarding why handedness may (or may not) be beneficial, and why it may have established itself as such a persistent trait (in humans).
There is currently no explanation as to why right handedness has become dominant over left handedness.
Note that 'handedness' has been identified in many other lifeforms, including mammals such as dogs and horses, reptiles such as snakes, and even in plants (some climbing plants with spiral tendrils consistently twirl in the same direction)
Further reading: Is handedness determined by genetics? US National Library of Medicine
Also see; Wikipedia and the specialist journal Laterality