Level of fixation
Today's nine Enneagram personality types evolved from Oscar Ichazo's nine ego-types which identified nine types of ego fixation. The goal of working with ego fixation was to find freedom from it, to realize it's not who you are but a habit of being that you've fallen asleep to. In other words, to begin "waking up" from the fixation.
The more asleep to or trapped in the fixation you are, the more limited your approach to life and the more unhealthy you may become psychologically. The reason for this is that you are limited to only the possibilities offered by your Enneagram type, operating from it even when it's inappropriate for the situation because it's all you know.
To begin seeing beyond the fixation allows you to be more adaptable in the way you respond to situations and more accepting of other ways of being (i.e., other Enneagram types). You can begin to explore who you are beyond your habit of being by adding choices that you didn't have when you were operating from a more unaware and unconscious place.
Simply put, fixation leads to limitations and psychological unhealth while freedom from fixation leads to adaptability and psychological health.
Levels of Development
Don Richard Riso detailed nine levels of development or health for each type. In general, levels 1-3 are said to be in the healthy range, 4-6 are in the average range, and 7-9 are in the unhealthy range.
A person is described as operating within a range of levels where the expression of type can seem to vary as they move between levels. In other words, there isn't simply one set of characteristics for a type but different characteristics for each level of development.
For example, two people may both be primary type 2. One person may be operating at the relatively healthy levels of 2-4 (empathetic, supportive, well-intentioned) while another person might be operating at the relatively unhealthy levels of 6-8 (self-important, self-justifying, entitled).
For Riso the levels of development add a vertical dimension (nine levels within each type) to the existing horizontal dimension (the nine types themselves).