It is purely a measurement of angle - essentially how many pixels the star moved and how many arcseconds/pixel the camera+telescope is measured to have.

Previously the stars were measured one at a time with a transit telescope so the angle was directly from the encoder on the declination axis (think vertical) and a clock for the right ascension (direction the stars rotate past a fixed point as the Earth turns).

Now most are measured with astrometric satellites like Hipparcos and Gaia. These have telescopes with a very well calibrated angle scale (pixels/arcsec). If you assume the most distance stars are fixed then you can measure how the foreground star appears to move relative to the same background stars in measurements 6months apart. You know the satellite has moved 2au around the sun and you can measure the angle difference to the star in arcsec, from the pixel movement relative to the background in the 2 images. You have then distance to the star in parsecs.

*(Sorry the previous point about 2 fixed telescopes measuring pairs of stars is an implementation detailed which complicated the answer)*