A lien on your property usually acts as a barrier when you are trying to sell something. When you “avoid” a lien, you obtain a judicial determination that the lien no longer encumbers a piece of property. This means that you would then be able to sell the property despite the lien.
For example, suppose that you own Blackacre, your ancestral estate. It is presently worth $300,000, subject to a first mortgage of $180,000. Suppose that someone obtains a judgment against you for $30,000 and then obtains a lien against Blackacre. They are planning to force a sale of Blackacre in order to recover their $30,000, or else they’re planning on camping out at your next refinancing or sale in order to skim $30,000 off the top of whatever money you receive after the mortgage is discharged. Now you file bankruptcy, and let’s suppose that your state law provides a $200,000 homestead exemption. The judgment lien impairs that exemption (makes it less worthwhile). Therefore, the Bankruptcy code allows you to avoid the lien, which means you will emerge from bankruptcy with Blackacre free and clear of that lien. However, the mortgage lien still exists because the Bankruptcy Code does not let you avoid voluntary or nonjudicial liens.