Gaia's motives range from discovering extra-solar planets to detecting quasars, but its most important purpose, in my opinion, is to precisely measure the distance to over 200 million stars within our galaxy to an accuracy of 10%, and out to a distance of 30,000 light years, well beyond the Milky Way's galactic centre. These distance measurements are obtained through a process called stellar parallax, where the apparent motion of a star is observed compared to more distant background stars as the Earth moves around the Sun.
Credit: "Stellarparallax2" by Original uploader was Booyabazooka at en.wikipedia - Originally from en.wikipedia; description page is/was here.. Licensed under Public domain via Wikimedia Commons.
Not only will the precise determination of the distance to this many stars in the Milky Way provide us with a detailed representation of the structure of our galaxy, but parallax is the most important fundamental measurement in the cosmic distance ladder. The cosmic distance ladder (or CDL) is a series of methods for determining distances in the cosmos which are calibrated to each other to greater and greater distances. The first rung in the CDL is the distances within our own solar system, which have been determined to great accuracy with radar. Once the Earth-Sun distance is determined precisely, accurate parallax measurements can be made.
Credit: The Worlds of David Darling
The next rung on the CDL is a class of objects called a Standard Candles. These are objects which have a known brightness, and therefore, when their apparent brightness is observed, one can calculate how far they are (sort of like figuring out the distance of a car based on how bright its headlights look). A couple of famous examples of standard candles are Cepheid Variables and Type Ia Supernovae, which are used to calculate the distance to objects much further than can be achieved with parallax (such as with distant galaxies). However, in order to calibrate the intrinsic brightness of these objects, the distance to nearby standard candles must be computed via some fundamental measurement, such as parallax. Thus, having accurate parallax measurements for nearby objects allows astronomers to determine the distance to bodies which are much further away.
It becomes apparent, when the determination of distance to far-away objects must be calibrated in this way, that an error in a lower rung of the CDL can seriously affect the distance measurements to very faraway galaxies. This problem became clear in the early 20th-century when Edwin Hubble was making his first distance measurements to nearby galaxies. When he discovered that the Universe is expanding, he calculated the age of the Universe to be only about 2 billion years, which was a problem because the age of the Earth had been estimated to be at least 3 or 4 billion years! This was later resolved when the brightness of Cepheid Variables was properly calibrated, which more than doubled the calculated age of the Universe. We now know the age of the Universe to be 13.8 billion years, and the value is mostly obtained from the distance measurements of far-off galaxies.
In conclusion, accurate distance measurements to objects within our own galaxy can have implications for our understanding of the history of the Universe! Even though the primary purpose of Gaia is to map out the structure of our galaxy, it will have a great impact on our knowledge of cosmology.