Booyakasha comes from the Irish word "buíochas" (pronounced bwee ah kuss) which mean "glory to" "or praise be" as in "buíochas le Dia" which means "thanks be to god". Oliver Cromwell sent 1000s of Irish to the plantations in Jamaica, and a lot of Irish (or Gaelic as non Irish people know it) words made it in to Jamaican patois. Another example is "Irie" from the Irish verb "Eirigh" (pronounced "Ire - ee") meaning to get up.
Don't know what it means but Ali G didn't make it up. Rapper KRS-One shouts it out at the beginning of "Keep Their Heads Ringin'" by Dr. Dre. In 1995. Before Ali G. Probably Jamaican roots then...
The term 'Booyakayashakaya' is often a term unknown to the world, but known to a limited group of people, unfortunately. The term can define anything, from people, to emotions, to defining the randomest of situations in one simple shout.