The current oath (taken by new citizens) includes a promise to "support and defend the Constitution and laws of the United States of America against all enemies, foreign and domestic". Who does that "domestic enemies" bit refer to? Commies? Anarchists? Confederates?
The first recorded oath of allegiance was by Lt. James Glentworth at Valley Forge. While he didn't designate any of the people he'd defend the United States from as "domestic", during the war there many loyal to the Crown of the that could fall under his "adherents" and "abettors". Following that, there was no requirement in the oath to do so.
The Naturalization Act of 1906 added the "foreign and domestic" enemies part to the oath. At the time there was concerns about Anarchists (McKinley was assassinated in 1901 by Leon Czolgosz, an Anarchist) so this might be a group targeted.
Our domestic enemies have change over time and this may be a set of terms added in while looking back at history and realizing that some in our country do not love our country and wish it harm. We as citizens should be charged with protecting it and this is just a reminder of that for our new citizens.