I've never seen this term, and I'm wondering what it means, with regard to ST_Polygonize

NOTE: Input linework must be correctly noded for this function to work properly

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this page helpfully shows some of the edge cases where this function would fail and return NULL. To summarise some examples...

  • two linestring geometries which touch/cross at one point. but don't loop back on each other to touch/cross at another point
  • two disjoint lines
  • a single linestring which does't form a complete loop

or any case where the set/array of geometries doesn't form one or more polygons. Also, rounding/precision errors might come into play, and it may be that linestrings need to align in a consistent direction.

there may be other definitions of 'incorrectly noded' :)

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