If I recall correctly, they just locked the selector in "semi", so the soldier couldn't move it. Replacing the selector switch with an unlocked one returns the M-14 to selective fire.
I found this on Wiki:
The M14M is a semi-automatic only version of the standard M14 and was developed for use in civilian rifle marksmanship activities such as the Civilian Marksmanship Program. M14M rifles were converted from existing M14 rifles by welding the select-fire mechanism to prevent full-automatic firing. The M14NM (National Match) is an M14M rifle built to National Match accuracy standards.
The M14M and M14NM rifles are described in a (now-obsolete) Army regulation, AR 920-25, "Rifles, M14M and M14NM, For Civilian Marksmanship Use," dated 8 February 1965. Paragraph 2, among other things, stated that the Director of the Alcohol and Tobacco Tax Division, Internal Revenue Service, Department of the Treasury (predecessor to the Bureau of Alcohol, Tobacco, Firearms, and Explosives) had ruled that M14M and M14NM rifles so modified would not be subject to the 1934 National Firearms Act (NFA) and, as such, could be sold or issued to civilians. However, with the passage of the Gun Control Act of 1968, the NFA was amended to prohibit sales of previously modified automatic weapons such as the M14M and M14NM to civilians.