I'll preface this ridiculously long answer by echoing the OP of answering with disinterest.
The Gemara only ever uses the term guf naki when discussing someone putting on tefillin. There are two main ways that the Talmudic sages and broader rabbinic literature have understood the term "a clean body":
As a Spiritual Condition
For the Meiri (Beit HaBechirah, Brakhot. 14b) the meaning of a "clean body" goes beyond physical issues (i.e., sleeping, dirtiness) to include a kind of spiritual cleanliness:
שהן צריכין גוף נקי מעבירות ומהרהורים ואין ראוי להניחם אלא לאחר התשובה וקצת חכמים נוהגים להניחם בימים שבין ר"ה ליום הכפורים אחר התשובה והטבילה והוודויין וכן הדבר נכון בעיני
...that they need a "clean body" from transgression and impure thoughts, and so it is not proper to put on tefillin until after one's repentance. And there was a custom for a few of the sages to put on tefillin during the Days of Awe (between Rosh Hashanah and Yom Kippur) after repenting, immersing in a mikveh, and saying vidduy, and this is the proper way in my opinion.
This definition goes beyond Talmudic sages Abaye and Rava's interpretation that people wearing "tefillin require a clean body like Elisha, the man of wings" (Shabbat 49a), which they respectively understand to mean an avoidance of flatulence and sleep (the latter being a time when flatulence and other unclean states occur). For the Meiri, the story of Elisha would suggest that righteous people, or those who become righteous through proper repentance, are the kind of people fit for wearing tefillin.
According to the Maharshal (Yam Shel Shlomo Kiddushin 1:64), this is part of why the sages did not protest Michal, the daughter of King Saul, because she was a "completely righteous person." For the Maharshal, then, having "a clean body" partly involves being a righteous person. Arukh HaShulchan (OC 38) similarly identifies "a clean body" as a physical, yet also spiritual, state, writing that Michal was righteous, and most women don't meet the requirements.
As a Physical Condition
Most rabbinic scholarship, however, understands "a clean body" in the simpler sense of meaning a tangible, physical condition of cleanliness, related to the standards of avoiding filth during the time of prayer. This follows the Talmudic understanding of the term, which implies a more achievable state for the individual. Regarding women, some have understood the problem with maintaining "a clean body" to be related to menstrual blood (cf. Maharam in Tashbetz 270). Such an argument appears to be about the issue of getting menstrual blood on the body, but this is hardly spelled out.
Instead, many poskim writing about women and tefillin, repeat Tosafot's wording that women "are not diligent about maintaining a clean body," without going into detail about what the problem entails (cf. Kol Bo 21; Eliyah Rabba OC 38:2; Mishnah Berurah OC 38:3, note 13).
Even though the nature of this cleanliness is seldom specified, some have written that this physical condition has to do with a cultural period of women being less hygienic than men. Eliyah Rabba, for example, writes:
ולי מסתבר דדורות אחרונים החמירו בזה, כי ראו שאין הנשים בזמן הזה זריזות כל כך, לכן החמירו למחות בכולן שלא יצא תקלה ממנו:
It seems to me that being stringent in the later generations [after the Talmudic era] has to do with the fact that women these days are not so diligent [about cleanliness], and this is why there is a stringency to protest their wearing tefillin.
This implies that women can potentially attain "a clean body," and Magen Avraham (OC 38:3) says as much:
מפני שצריכין גוף נקי ונשים אינם זריזות להזהר אבל אם היו חייבים לא היו פטורין מה"ט דהוי רמי אנפשייהו ומזדהרי כנ"ל דלא כע"ת
[We protest] because they need a clean body and women are not diligent about being careful. But if they were obligated to wear tefillin, they wouldn't be exempt for this reason. Rather, they would need to take the risk and be more careful [to maintain a clean body].
Summary
"A clean body" may mean some kind of spiritual requirement to be like Elisha (who was righteous enough to have miracle protect him from a Roman guard). If so, than this difficult-to-quantify level may be a further limiting factor for people already not obligated in the mitzvah. Alternatively, "a clean body" could be a general term for physical states of uncleanliness (e.g., flatulence, feces, etc.), and/or particular to women (i.e., menstrual blood on the body), which may hinder women from wearing tefillin because they were once, apparently, less diligent in its maintenance.
For practical application, CYLOR and perhaps, your personal hygienist.
