Although the Enneagram circle originally had a different purpose, with the the nine personality types the circle can be used to explore the influences and commonalities between the types. Some ways this is done is by looking at adjacent types, opposite types, triads, and movement along the inner lines of the symbol.
It is sometimes said that a type is the product of the two types on either side as seen on the circle of the Enneagram symbol. Type 9 could then be thought of as a product of types 8 and 1.
Looking at this another way, the types on either side have a unique influence upon the type in the middle. This forms the basis of the wing theory in the Enneagram personality type system which suggests that adjacent types have a strong influence upon the type in the middle and one of the two has a stronger influence.
Taking type 9 as an example, types 8 and 1 are said to have a strong influence upon someone who identifies as type 9. Furthermore, one of the two wings (type 8 or 1) will have a stronger influence and be referred to as the preferred wing (9w8 or 9w1).
The concept of antipodes is briefly discussed by Claudio Naranjo in his book Character and Neurosis. He draws similarities between the types opposite one another on the circle.
The three antipode pairs are: 1-5, 4-8, and 7-2. Types 3, 6, and 9 have no antipodes (though these three types can be compared with each other).
Refer to Naranjo's book Character and Neurosis for more.
The nine personality types are often grouped into a set of triads (three groups of three types). The most common set of triads is the centers of intelligence, but there are other sets of triads as well.
The triads explore commonalities between the types in each group. For example, types 891 are said to be gut or body types, types 234 are heart types, and types 567 are head types.
The lines and arrows suggest influences or movement between the types around the circle such as: connecting points, stress/security points, and directions of integration/disintegration.
Metaphorically we can look at the Enneagram circle and the nine types placed around that circle as a representation that we are in reality all nine types. It's just that we got stuck or fixated at one point.
The original purpose of the types was to identify where we're fixated and work to find freedom from that fixation. As the Enneagram personality types gained in popluarity, that original purpose has been lost to many.