The Enneagram is a symbol / diagram with nine numbers ("ennea" means nine). Although the Enneagram was originally used for a different purpose, today the nine numbers are commonly associated with nine personality types.
The numbers when used with the personality types have two purposes:
The values of the numbers don't have any meaning in regard to the types. In other words, type 1 is not any better than type 2 and people don't move from being a type 1 to being a type 2 to being a type 3, etc.
It can seem a bit strange when first hearing people refer to themselves or others as numbers (e.g., I'm a 1 and she's a 2). But there are some advantages to referring to the types by number.
There is no single authoritative description of the types. There are as many interpretations as there are people teaching and learning about the types. Different Enneagram schools use different word labels for the types.
For example, one school of the Enneagram types may refer to type 1 as the Perfectionist, while another as the Reformer, and another as the Good Person, etc. It can sometimes be difficult to track which type is being talked about when using these word labels.
By contrast, referring to type by number not only makes it obvious which type is being talked about but removes any bias introduced by the interpretation's label.
In addtion, the word labels tend to emphasize only one aspect of a type. If someone relies too much on the word label then they risk a very limited and sometimes stereotypical understanding of the type.
Someone might say for instance "I must be a type 1 because I'm a perfectionist" when the reality is that people of different types can be perfectionistic. You aren't a type 1 just because you have perfectionistic tendencies.
You may also hear something like "she can't be a type 1 because she's not a perfectionist" when perfectionism may or may not be how type 1 gets expressed through personality for a particular individual.
Also, since the numbers are used to place the types on the symbol, it can be easier to visualize other concepts that can be seen on the symbol by referring to the types by number.
Wings for example are the types on either side of a type as seen on the symbol. It's easy to remember type 2's wings are types 1 and 3 but not so easy to remember that the helper's wings are the perfectionist and the achiever.