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...
Fer Booyakasha mean a right many fings. But like fer da most part its a greetin innit. Iz use it all da time wit me posse.An When Me iz nobbin J Lo. straight up me aignt shitin you. Yo shout out bredren. Iz out Frek mez, Flamez.
Booyakasha Mez aboot ta talk to me rude boy ere about da Mac Daddy, Ronald McDonaldz aight.