According to the Rutherford Institute, the importance of the Third Amendment is that it prevents the military from entering the private property of civilians during peace time. The amendment also limits the use of private property by the military in war time. The only exception is in cases pertaining to national security.
The Third Amendment helps to protect the privacy of American citizens and safeguards homes from military intrusion. The Rutherford Institute further notes that the Third Amendment demonstrates that civilian authority is greater than military authority. The Third Amendment was originally designed to help protect the rights of landowners previously subjected to military officers forcing them to provide housing for the military.
According to LAWS.com, this was an issue during the Revolutionary and Civil Wars when soldiers did not have a base in which to shelter. Under the Third Amendment, a soldier has the right to ask for permission to stay on someone's personal property during wartime. However, the military cannot seize the property or demand that shelter be given to soldiers.
According to the Annenberg Classroom, the only time a landowner's rights are overridden involuntarily is if military occupation of the property is in the best interests of national security.