Question

What is a unified atomic mass unit? How is it equivalent to 1 g/mol?

Answer 1

The unfied atomic mass unit is defined as the mass of exactly 1/12 of the mass of an atom of the carbon-12 isotope.

Explanation:

This means that exactly 12 grams of pure Carbon-12 is exactly 1 mol.
Determining all other atomic or molecular masses uses this as a yard stick.

At first realative atomic mass was related to hydrogen as being 1, but as the presence of H-2 in hydrogen varied, they later used oxygen-16 as being 16.
For practical reasons, carbon-12 as being exactly 12 proved to be better (easier to handle than the gases).
The difference between the systems are small, and for most chemical calculations they are beyond signifance level.