Although many schools of the Enneagram personality types use the inner lines to identify connecting points not all of those schools use the arrows.
The lines with the arrows
The two most prominent schools of the Enneagram personality types (The Narrative Enneagram and The Enneagram Institute) give meaning to the arrows.
The Narrative Enneagram describes movement with the arrow as toward a stress point while movement against the arrow is toward a security point.
Security and stress points show where our energy and awareness flow, depending on our needs and circumstances. We often move from our “home base” to the two points connected to our own by the lines in the diagram. The stress point is where we go when feeling stressed and pressured, or when mobilizing for action. The security point is where we go when feeling relaxed or secure, or paradoxically, when feeling overwhelmed or exhausted. This dynamic movement creates a significant shift in our point of view and style of behavior, allowing us to become less stuck in our habitual patterns.
(from the narrativeenneagram.org website)
For example, type 1 in stress will go to type 4, but type 1 in security will go to type 7.
The Enneagram Institute describes movement with the arrow as the direction of disintegration (stress) and movement against the arrow as the direction of integration (growth).
The inner lines of the Enneagram connect the types in a sequence that denotes what each type will do under different conditions. There are two lines connected to each type, and they connect with two other types. One line connects with a type that represents how a person of the first type behaves when they are moving toward health and growth. This is called the Direction of Integration or Growth. The other line goes to another type that represents how the person is likely to act out if they are under increased stress and pressure—when they feel they are not in control of the situation. This second line is called the Direction of Stress or Disintegration. In other words, different situations will evoke different kinds of responses from your personality. You will respond or adapt in different directions, as indicated by the lines of the Enneagram from your basic type.
(from the enneagraminstitute.com website)
For example, type 1 under stress will move in the direction of disintegration to type 4, but type 1 will move toward health and growth in the direction of integration to type 7.
Both approaches are similar but the directions of disintegration / integration also tie back to the levels of development in that there's a movement between the types at the same level of development.
The lines without the arrows
The reason the arrows are pointing as they do on the Enneagram symbol predates the personality types use of the symbol. The types simply used the arrows as they were without any additional rationale for why they mean what they mean. In other words, you could just as easily make a case for the opposite where stress is against the arrows and growth/security is with the arrows. As such, many people use the lines without regard to the arrows as indicating another influence upon or movement for type calling them connecting points.
As an example, type 1 can be looked at as having an influence from types 7 and 4 or, put another way, type 1 can be seen to move to types 7 and 4 at times without describing that movement as one of stress or growth.
The arrows themselves are most often not shown on the symbol for the Enneagram types anyway. They're usually only shown when someone is emphasizing the concept of stress vs. growth / security or something similar.