The way the brain works is incredibly complex, but this simplified explanation will give you some understanding of where our left-hand dominance comes from. The brain is "cross-wired" so that the left hemisphere controls the right handed side of the body and vice-versa and hand dominance is connected with brain dominance on the opposite side - which is why we say that only left-handers are in their right minds!

Exposure to higher rates of testosterone before birth can lead to a left-handed child. This is the Geschwind theory, named after the neurologist who proposed it, Norman Geschwind. It suggests that variations in levels of testosterone during pregnancy shape the development of the fetal brain. Testosterone suppresses the growth of the left cerebral hemisphere and so more neurons migrate to the right hemisphere.