The "push and pull" refers to an energetic phenomenon that occurs in a twin flames dynamic.
The Soul energy is pulling together its two incarnated aspects like magnets. An incredible, unstoppable force is naturally drawing in the two Flames together, at least energetically. This is the "pull". Sometimes it is felt by one at the heart Chakra when the other is sending love vibes, other times it can be felt at the sacral Chakra when the sexual energy becomes stronger.