Yippie ki yay is an exclamation of joy that was popularly used by US cowboys in the mid 19th century.
You probably remember the scene where the line is first uttered. As McClane makes contact via walkie-talkie with Hans Gruber (Alan Rickman), a master criminal who’s led a team of thieves to seize L.A.’s Nakatomi Plaza, the villain questions this cop’s motivations — and his identity. “You know my name,” Gruber says, “but who are you? Just another American who saw too many movies as a child? Another orphan of a bankrupt culture who thinks he’s John Wayne? Rambo? Marshall Dillon [from Gunsmoke]?”
Unimpressed, Gruber asks snidely, “Do you really think you have a chance against us, Mr. Cowboy?” McClane knows he’s outnumbered and outgunned. It’s going to take a miracle to save the hostages, including his estranged wife, Holly (Bonnie Bedelia), and himself. But he’s arogant, and there’s just something so incredibly patronizing about how Gruber refers to him as “Mr. Cowboy.” So it’s right then that McClane unveils what would become his trademark quip, and one of the great retorts in blockbuster history: “Yippee-ki-yay, mother******.”