Final answer:
The centrosome is the microtubule-organizing center in animal cells, consisting of two perpendicular centrioles made up of cylindrical microtubule triplets.
Step-by-step explanation:
The microtubule-organizing center in an animal cell is the Centrosome. The centrosome is located in the vicinity of the cell's nucleus and consists of a pair of centrioles, which are arranged perpendicular to one another. Each centriole is structured as a cylinder made up of nine triplets of microtubules. In essence, all microtubules within the cell originate from the centrosome, which plays a crucial role during cell division by organizing the mitotic spindles.