The word is a combination of not +Nazis. The characters represented in the films1 are, or might be considered, Nazis (see Controversy below) but the figures are stripped of any insignia or markings which might identify them as such.
An early use of the term was in a discussion on Eurobricks in late 20072 before the sets were released worldwide. Spoken aloud the term sounds almost identical to nazis3 but when written on internet message boards and web pages the difference is clear.
The time-frame of the films in question is during the reign of the Nazi party in Germany. To recreate the soldiers accurately LEGO would have had to reproduce insignia that included the Nazi swastika. Illegal in Germany and particularly offensive to those living in what was Occupied Europe LEGO has chosen not to reproduce any identifiably Nazi symbols.
It might also be noted that these figures represent the first modern soldiers created by LEGO. Before this the most modern soldiers were Union soldiers from the American Civil War era. LEGO has always been reluctant to introduce modern weapons into sets but has been more willing to do so in licensed sets4. As recently as 2001 they created two distinct versions of the same theme with a North American version containing guns while the European version did not5
1 - The first series of sets released in late 2007 were based on Raiders of the Lost Ark and Indiana Jones and the Last Crusade. The less popular Indiana Jones and the Temple of Doom was not represented with any sets in that initial series.
3 - making it also a pun.