According to Numbuh 5, the Fourth Flavor was a flavor of ice cream that existed along with the three original flavors chocolate, vanilla, and strawberry. It was so delicious, that most people were deemed unworthy to taste it, so it was hidden away. A golden jewel encrested scooper served as a key to obtaining the Fourth Flavor. In Operation: F.L.A.V.O.R., it and Abby were taken by the Delightful Children From Down The Lane to use her knowledge to help them and the Ice Cream Men reach it. The way to the Fourth Flavor was riddled with traps including a riddle that had to be answered correctly or you would be chocolate coated, a giant crushing scoop of ice cream, and others. When they finally reached the mound of ice cream, the Delightful Children had the men collect it to give it to the adults in an exclusive party. Before that, they planned to be the first to taste the Fourth Flavor in generations. But by adding sprinkles to perfect ice cream, the entire temple began to collapse around them, and the Fourth Flavor is lost. At the end of the adventure, Numbuh 5 discovers just a small amount of the gold colored treat on her hat. Before she could say what it tasted like, Numbuh 1 interrupted her by contacting her on the radio. Satisfied in having at least tasting the ice cream, she left the temple behind.
When he was recommissioned, Numbuh 0 felt a craving for blurpleberry ice cream, claiming it to be the closest thing to the actual Fourth Flavor he ever tasted, revealing that he was deemed worthy to partake of the legendary flavor. Also, it may hint that the Fourth Flavor was similar to blurpleberry.
Or he could be refering to it on religious terms, like when someone says "This tastes heavenly."
Numbuh 5 and the DCFDTL are the only known characters in the series that had tasted the Fourth Flavor.