"'Have you not just called to me: "My Father, my friend from my youth, will you always be angry? Will your wrath continue forever?" This is how you talk, but you do all the evil you can.'" NIV translation
The people's actions did not match their words or their faith. They called out to God as Father but did not listen to the words of the Father or to His correction. This is even more widespread today as there has been great numbers of people come to God and acknowledge Him as Father yet do not have a daily walking relationship with Him through Jesus Christ. This demonstrates the true nature of "backsliding" as it is not an accidental stumbling but an out right defiance of following God's direction. It is much like what happens when you try to move a small cow or calf that does not want to be moved. They dig in their front feet and sit down on their hind quarters. It is virtually impossible to move them forward until they are ready to stand up again. This is the same thing that is happening with God's people, in that, He is waiting for us to decide to stand up where we can then be moved by Him in His direction.
"During the reign of King Josiah, the Lord said to me, 'Have you seen what faithless Israel has done? She has gone up on every high hill and under every spreading tree and has committed adultery there. I thought that after she had done all this she would return to me but she did not, and her unfaithful sister Judah saw it.'" NIV translation
King Josiah was a king over the land of Judah and led a great revival of the faith. During this time, God pointed out the backsliding of the northern kingdom (Israel) and the fact that they knew they were to go to Jerusalem to worship but refused. The people of Judah saw that people from the northern kingdom no longer came to Jerusalem for worship.
"'I gave faithless Israel her certificate of divorce and sent her away because of all her adulteries. Yet I saw that her unfaithful sister Judah had no fear; she also went out and committed adultery.'" NIV translation
At this time, the northern kingdom (Israel) had been conquered and taken into exile. That is like a certificate of divorce in that God did not protect her anymore as a husband protects his wife. The southern kingdom (Judah) witnessed this and yet did not fear God but followed false gods as well. This verse speaks of the impact that our personal walk with the Lord can have on others around us. This impact can be negative as we see it was here with Israel and is sorta like what is commonly called carnal Christians. This is where those around you know that you go to a "church" regularly but they also see that, once you leave that building, you run after wealth, fame, or some other idol. If that describes you or someone you know, then, like Israel, you/they are backsliding.