If you and a friend aren’t talking to each other, your relationship is strained. To repair your friendship, a reconciliation is needed. This may occur through a third-party or at the initiation of you or your friend.
In the spiritual realm, we have a strained relationship with God; we have been separated from him as a result of our bad behavior. He desires to have our relationship repaired. This has been done by Jesus and if we accept his efforts, we are reconciled to God, the Father.
This is what the Bible means when it talks about reconciliation.