What goes into a muhurat
The five angas come first: tithi, nakshatra, yoga, karana, and the weekday. Different activities prefer different combinations. Vivah muhurat traditionally favours particular nakshatras and avoids others entirely, while griha pravesh has its own preferred set.
Next comes the rising sign for the moment itself, because a muhurat chart has a lagna just as a birth does. The lagna and the position of the Moon at that moment shape whether the window is considered supportive for the activity in question.
Finally, inauspicious periods are excluded. Rahu kaal, gulika kaal, and yamaghanta shift daily with sunrise, and bhadra or vishti karana is avoided for auspicious beginnings. A window that clears all of these is what the tool reports.