Triangulation from opposite sides of Earth's orbit
Parallax is the apparent shift in a star's position when viewed from opposite sides of Earth's orbit six months apart. Nearby stars show larger shifts than distant ones; the angle of shift reveals distance through trigonometry. A star at one parsec (3.26 light-years) has a parallax of exactly one arcsecond, a unit that defines the parsec. More distant stars have smaller parallax angles and are harder to measure.
The measurement requires precision. A one-arcsecond angle is smaller than the angle subtended by a coin at a distance of 4 kilometers. Ground-based telescopes can measure parallax to roughly 100 light-years; the Hipparcos satellite (1989-1993) extended this to 1,000 light-years. Gaia (launched 2013) measures parallax for over a billion stars to distances of 30,000+ light-years, mapping Milky Way structure in unprecedented detail.
The foundation of the cosmic distance ladder
Parallax is the first rung of the distance ladder because it requires no assumptions about the object being observed. It is pure geometry: if you know Earth's orbit size and can measure an angle, distance follows. All other distance methods (Cepheid variables, supernovae, redshift) are calibrated by comparing their properties to parallax-measured objects.
Once parallax distances were known for nearby Cepheid variables, astronomers could measure Cepheids in other galaxies and infer those galaxies' distances. Cepheids then calibrated supernovae distances, extending the ladder to the edge of the observable universe.