2-way connection means that both sides of the connection - channel manager and PMS - are required to accept data from the other side in order to correctly connect a PMS through channel manager to all the channels.
So both sides need to have an open API which the other side has to connect to.
Channel manager side accepts Inventory updates (prices, availability, restrictions), booking confirmations and property content (property description, images, rate policy, etc.).
PMS side accepts bookings.