The five limbs of the day, and the electional use made of them
A pañcāṅga is literally a five-limbed description of a moment: tithi, vāra, nakṣatra, yoga and karaṇa. Four of the five are computed from the relation between the Sun and the Moon alone — only the weekday is independent of them — which is why the whole apparatus can be tabulated in advance and why almanacs have existed for as long as the tradition has.
Muhūrta is the applied side: choosing a moment whose five limbs suit the undertaking. The logic is that a beginning inherits the character of the sky it begins under, so a chart cast for the moment of starting behaves like a birth chart for the enterprise. The commonest failure in practice is optimising the five limbs while ignoring the lagna — a beautiful tithi with a ruined ascendant is a bad muhūrta.