She will either approach you, or if she doesn't she has given a non-verbal signal that she is open to being approached.
With flirting, eye contact will never be the whole interaction, but it is a very powerful opening interaction.
Avoiding her eyes shows that you aren't comfortable with the sexual tension and that you won't be able to handle her.
If you hold your gaze when a woman looks at you then it opens the door.
You have demonstrated your confidence and character and shown that you are in fact comfortable with the sexual tension.
By looking someone in the eye upon first meeting them you gain an impression into their character.
Using eye contact for flirting is just an extension of what we normally do anyway. Low risk in that the flirting can get started without you having to talk or without you having to approach.
It demonstrates that you really value what they are saying and that you are genuinely listening.