Reconciliation is a homely word for making up after a quarrel. This is done by taking away the cause of the quarrel; unless this is done, there may be an uneasy truce -but there can be no real reconciliation.
In the hostility between God and sinners (Rom 5:10), the root cause, sin, was put away by the death of Christ, and thus the way was clear for reconciliation.
Much the same is the expression “making peace” (Eph. 2:15); indeed, so closely is Christ involved in the process that he can be said to be “our peace” (Eph. 2:14).