The triads are used to group the nine types into three groups of three. Each group is called a triad. The centers are the most commonly used set of triads with the personality types.
A set of triads is used to contrast the types using concepts containing three elements (one element for each of the three triads). For example, types 2, 3, and 4 are in the heart-based center while types 5, 6, and 7 are in the head-based center. Types 2, 3, and 4 are seen to share something in common (heart-based) while they are also contrasted with the head-based types (234 vs. 567).
The triads are often used to fit new concepts or theories into the system (e.g., Karen Horney's detached, compliant, and aggressive types; object relations groups; id, ego, and superego, etc.). Sometimes these introduced concepts or theories are widely accepted by teachers. Other times they are exclusive to the interpretations of a particular teacher or school. Still other times they are only debatable possibilities being explored.
More details about the triads can be found in the Enneagram User Guide series book Decoding the Enneagram. This book explores the four sets of triads commonly used with the personality types. Check the home page for the latest information about the availability of this book, other books, and related projects.