"This is what he showed me: The Lord was standing by a wall that had been built true to plumb, with a plumb line in his hand." NIV translation
Now, the prophet sees a wall that has been properly built and the Lord standing by it holding a plumb line. The plumb line is a tool that is used during construction to make sure that something is straight up and down. It usually consists of a weight that is attached to a string. The string is tied to the top of something and gravity acting on the weight stretches the line out perfectly straight.
The Lord told Amos that the plumb line was going to be used to judge His people. They were like the wall that had been built straight but are now going to be checked to see if it is leaning.
"'The high places of Isaac will be destroyed and the sanctuaries of Israel will be ruined; with my sword I will rise against the house of Jeroboam.'" NIV translation
Israel was clearly not straight with God and so judgment is proclaimed. As we see, here, the judgment begins with the leadership which was king Jeroboam.
"Then Amaziah the priest of Bethel sent a message to Jeroboam king of Israel: 'Amos is raising a conspiracy against you in the heart of Israel. The land cannot bear all his words. For this is what Amos is saying: "Jeroboam will die by the sword, and Israel will surely go into exile, away from their native land."'" NIV translation
Amaziah was a hired preacher and usually said what the king wanted to hear. He was not of God and he lied about what Amos was saying. He was simply calling the leaders of Israel to turn away from their golden calf and turn back to the ways of God. It is much the same way today as many "churches" have strayed far from the ways of God. Many "pastors" will simply say what the congregation wants to hear instead of what God wants them to hear. When a man of God calls them to turn back to the ways of Jesus, their leaders will lie and act in the same manner as Amaziah.