why "amu" is used as a unit in relative atomic mass?
$$
\pu{1 u} = \pu{1.660539040(20) \cdot 10^{-27} kg}
$$

The u (amu is the old unit name) is $1/12$ of the weight of an $^{12}\ce C$ atom.

The way the u is chosen ensures that all core and atom masses are multiples of 1($\pm $0.1) u. The u is a count of nucleons in an atom. 

Until the 60s, chemists used $1/16$ of the mass of a average atom in a oxygen-isotope-mixture and physicist used $1/16$ of the mass of a $^{16}\ce O$ atom. 

It's really just about choosing what is the best to measure and have a consistent result with. So you would chose an element with a very consistent isotope ratio (isotope-pure $^{12}\ce C$ e.g.) and one where you can measure weights easily.