Fortunately, parallax was found, for without parallax, we wouldn't know which stars are nearby and which are far away. Thus, if you divide the Moon into 1800 pieces, you'll get 1 arc second. Through the trigonometry of the extremely skinny triangle, we can then measure a distance.
Astronomers always try to make things as easy as possible for themselves.
To make things easy, they define a new unit of distance, called the parsec. One parsec is the distance a star would have if it had a parallax angle of 1 arc second. Note that by defining a parsec in this way, the relationship between the measured parallax angle and the implied distance is trivial. If a star has a parallax of 1 arcsec, its distance is 1 parcsec. And so on.