What is fix geometry actually doing in QGIS?

I think @Vince's idea is what you can try.

From QGIS Documetation:

Attempts to create a valid representation of a given invalid geometry without losing any of the input vertices. Already valid geometries are returned without further intervention. Always outputs multi-geometry layer.

More details you can find in:

• qgsalgorithmfixgeometries.h
• qgsalgorithmfixgeometries.cpp

P.S. I hope that @Nyall Dawson will answer this question.

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References:

• Docs » QGIS User Guide » 23.1.15.32. Fix geometries
• GitHub/QGIS/src/analysis/processing/

It is basically fixing your geometry using the makeValid method, that is, correcting your geometry without loosing nodes:

https://qgis.org/pyqgis/master/core/QgsGeometry.html?highlight=qgsgeometry#qgis.core.QgsGeometry.makeValid

similar of the St_MakeValid of PostGIS:

https://postgis.net/docs/ST_MakeValid.html

As per the OGC Simple Feature Access specification, geometries need to follow the OpenGIS compliance (see the PostGIS docs for quick reference), where (listing only the most prominent predicates)

• Points are considered inherently valid
• LineStrings are valid if they are simple, meaning that they don't pass an inner vertex twice
• Polygons are valid if their linear components are simple and none of their rings cross
• MultiPoints are valid if no coordinate pair is present twice
• MultiLineStrings are simple if all their components are simple, and common vertices only touch
• MultiPolygons are valid if all their components are valid and do not overlap

In order to do so, the internally called GEOS modules will (listing only the most prominent operations)

• correctly node a LineString and remove consecutive duplicated vertices
• correctly node the linear components of a Polygon and iteratively rebuild all possible valid areas from them
• do the above for all parts of their Multi geometries

where noding means breaking apart a linear component at non-consecutive duplicated vertices.

In this context, 'fixing' geometries rather means creating the maximal set of their valid and/or simple parts, and may result in a collection of geometries of different dimensionality.