Panchang means five limbs. Four of the five are precise astronomical quantities and one is a convention. Understanding which is which removes most of the mystery from a daily panchang.
Tithi — the angle between Sun and Moon
A tithi is the time the Moon takes to gain 12 degrees on the Sun. Thirty tithis make a lunar month. Because the Moon's speed varies, a tithi runs anywhere from about 19 to 26 hours, which is why tithis do not line up with days and why a date can carry two.
Vaar — the weekday
The only limb that is a convention rather than a measurement. The seven weekdays run in a fixed order and are ruled by seven planets, and the sequence comes from the ordering of planetary horas rather than from anything observable on the day.
Nakshatra — where the Moon is
The Moon's position against the 27 lunar mansions. It changes roughly once a day and is the limb most used in muhurat, because many activities are prescribed for specific nakshatras.
Yoga — the sum of the two longitudes
Add the longitude of the Sun and the Moon and divide the result into 27 parts. That is yoga. It is not the angle between them — that is tithi — and the two are often confused. Some yogas, notably Vyatipata and Vaidhriti, are avoided for new undertakings.
Karana — half a tithi
Each tithi is split into two karanas, giving 60 in a lunar month. Eleven karanas rotate through them: seven repeat, four are fixed. Vishti karana, also called Bhadra, is the one commonly avoided.
Why your panchang must know where you are
Every limb is anchored to sunrise, and sunrise depends on latitude and longitude. A panchang computed for Delhi is genuinely wrong for Chennai — often by enough to change which tithi is current at a given hour. Any panchang that does not ask for a location is showing you somebody else's day.
Four of the five limbs are pure geometry. Only the weekday is a convention.