MAH-teh. MAH like in malt, and -teh like in Gral. Patten.
Mate is a short form of Yerba Mate, whose leaves are dried and brewed into a caffeine-rich beverage similar to coffee and tea.
Yerba Mate contains roughly 85 mg of caffeine per 8-oz cup, which is just slightly less than the 94 mg of caffeine in an 8-oz cup of coffee.
Also see: how much caffeine in a cup of coffee.