Conversion is often associated with joining a new church (which I have done), but that's not what this vow implies. Conversion (conversatio) has to do with a cultivated attitude of turning: turning the soil of one's heart so it remains fertile, and turning perpetually back toward the sacred other in order to engage in dialogue. Conversion implies on-going resistance to one's own closed, hardened heart. Conversion requires ongoing engagement.
Conversion can be really tough.
Suppose my heart has been hardened by the scars of old wounds. Why would I reopen them by making myself vulnerable to God or my neighbor? Why would I risk an even greater wound?
The Benedictine life demands the risk of possible wounding so that one can love God and one's neighbor with abandon. The Benedictine vow of conversion is a vow to risk the cross in order to invite resurrection.
In what ways will I meet the cross during my novitiate? In what ways will I be raised up?