Astronomers used trigonometry to calculate the distance to stars long before the term parsec was coined, but the new unit made it easier to conceptualise unfathomable distances.
A parsec is the distance from the sun to an astronomical object which has a parallax angle of one arcsecond (1/3600 of a degree). The parallax angle is found by measuring the parallax motion (or apparent movement of a star relative to stable, more distant stars) when the star is observed from opposite sides of the Sun (an interval of six months on Earth). The parallax angle is obtained by halving the angular difference in measurements.
Once the parallax angle is established you can calculate the distance to a star using trigonometry, because we know Earth’s distance from the Sun. The distance from the Sun of a body with a parallax angle of 1 arcsecond was thus defined as a unit and, thanks to Turner, named the parsec.
With the parsec defined, deriving and describing huge distances became easy, since a distance in parsecs can be calculated as the reciprocal of the parallax angle in arcseconds (if the parallax angle is 1 arcsecond, the object is 1 pc from the sun. 0.5 arcseconds means the object is 2 pc distant).
The metre is a unit of length in the metric system, and is the base unit of length in the International System of Units (SI).
As the base unit of length in the SI and other m.k.s. systems (based around metres, kilograms and seconds) the metre is used to help derive other units of measurement such as the newton, for force.