Centrioles are cylindrical cellular structures that play key roles in organizing microtubules and guiding cell division, as well as contributing to the formation of cilia and flagella in many cells. They act as core components of the centrosome and help establish the spindle apparatus during mitosis, ensuring proper chromosome alignment and segregation. In non-dividing (interphase) cells, centrioles are involved in forming cilia and plays roles in signaling and motility. In summary, their main functions are:

• Organizing the pericentriolar material to nucleate and organize microtubules, forming the centrosome and the spindle poles during cell division [centrosome formation and spindle organization] (context based on general cell biology understanding).
• Serving as basal bodies to template the formation of cilia and flagella, enabling motility and signal transduction in specialized cells.

If you’d like, I can tailor this explanation to a specific organism (e.g., animal cells vs. plant cells, where centrioles are absent in most plants) or to a particular stage of the cell cycle.