An astrometric binary star is a binary star for which only one of its component stars could be visually observed. The visible star's position is carefully measured and detected to have a wobble, due to the gravitational influence from its counterpart.
From astrometric measurements of the movement of the visible star, the size and period of its orbit can be deduced. This can then be used to estimate the mass of the system.
This method of detecting binaries is also used to locate planets orbiting a star.