THESIS:
The meaning of the statement that a given law is Biblical (mi-de-Orraita) or rabbinic (mi-de-Rabbanan) is that it is a more critically important norm for life [for the human/Jewish condition] or a less critically important norm for life.
EXPLANATION:
To be sure, if the way that one was taught how to be human was via the guidance of the Biblical-Judean culture, anything strongly required for life is obviously demanded by God/Torah. There is no gap between the ancient Biblical-Judean tradition and the norms that one notices that real life demands. Nonetheless, there can be debates over the importance of a given norm. Is a given norm important enough to be equated with a Biblical law example that it parallels? Meaning, would one who taught the Biblical law also obviously intend that everyone treat the given norm just as punctiliously? If so, from the time of the Bavli Talmud onward, we express that point by stating that it is mi-de-orraita. Or is a given norm less critical that the Biblical law example that it parallels? Meaning, even if someone who taught the Biblical law would also obviously intend this given norm, would they not expect everyone to treat the given norm just as punctiliously? If so, from the time of the Talmud Bavli onward, we express that point by stating that it is mi-de-rabannan.
ILLUSTRATION (PROOF)
The best way to see this is by reviewing all the cases where rabbinic tradition correctly points out that an obligation that seems Biblically mandated from a syntactic reading of a given pasuk, is actually not what the pasuk meant -- is merely rabbinic. And the cases where they correctly point out that a norm that is not stated in the closest written Biblical law example was obviously intended by the pasuk -- such as not to accept hearsay evidence once the pasuk demands at least two to three witnesses.
The easiest way to see this, however, without reviewing all of the Talmud Bavli or my articles is to notice the laws of Shabbat.
1. The Tannaim already distinguished between violating the day of rest via serious work (מלאכה, מלאכה שיש עמה מחשבה, מלאכת מחשבת) that the Torah forbids so as not to impose labor on slaves, animals, and day laborers and violating the day of rest via less onerous work tasks and/or tasks that one can understand how a person might not easily forego for a whole day (שבות). {The meanings of these terms have been discussed in some of my publications and will not be repeated here.}
2. The Talmud Bavli (possibly the Babylonian Amoraim themselves), in turn, designates those more severe violations of the day of rest as Biblical and those less severe violations as Rabbinic.
3. Inasmuch as the Tannaim had not limited their exegetical discussions of Biblical verses to the more severe Shabbat violations but had made a commonsensical distinction anyway between severe and less severe violations of rest, the Bavli is simply expressing that distinction in its own cultural language.
4. As to why the Bavli uses that language -- from God versus from the rabbis -- that will have to be discussed in my history book.
