Think of it as a windmill. If you blow towards the windmill perpendicular to the windmill rotor plane (directly into the windmill rotor), you get a lot of rotation in the system. That same windmill, if you blow from the side, you won't get anything out of it.
Cyclic alters your attitude towards the airflow or if you will alters the relative direction of the airflow in relation to the rotor disc. Flare - increase of area-airflow, cyclic forward, decrease in area through which the airflow is going (just like blowing the windmill from the side.