The data was built by the Faithlife team. The Logos help file gives this very simple explanation:
The root is the core part of a word that gives it meaning.
If words are like houses, then roots are the foundation; they are what lemmas and inflected forms are built upon. For example, in English, words like biology, biography, and antibiotic are all built from the root bio. While each of these words have different meanings, they all, at their core, are concerned with life, which is what the root bio means.
Is that sufficient as an explanation, or do you need a more technical description?
Some lemmas are related to many possible roots and no explanation is given why such relations were established.
In addition to what Mark said, they are established by historical linguistics and descriptive morphology. An etymological dictionary is where one most often finds the full explanation. However, technical commentaries often contain relevant discussions.
I was looking for something like MJ. Smith mentioned: a bibliographic information or preferably a reference list. We may cite logos as a reference, but it does not add much to strengthen an argument, because logos does not provide "relevant discussions", as MJ. Smith already said.
Anyway I am very grateful for the help!