By precisely measuring its motion around the black hole, the researchers could compare its orbit with predictions laid out by classical Newtonian dynamics. They found that the star's actual orbit deviated from Newtonian predictions exactly as predicted by Einstein's general relativity – although the effect was slight.
In a nutshell, Einsteinian gravity treats space and time as two of the same – four-dimensional "spacetime" where time is another dimension incorporated into the three dimensions of space – and matter influences the curvature of spacetime while the curvature of spacetime influences the motion of matter. For example: If you have a massive object, it will bend spacetime, like the famous example of the bowling ball suspended on a rubber sheet. If another object travels past the massive object, the curvature of spacetime will deflect its direction of motion – like a marble rolling past the bowling ball.
Classical Newtonian gravity assumes space and time are separate dimensions and does not include the effects of the curvature of spacetime. Therefore, general relativity will leave an imprint in the motion of all moving objects in the universe (creating a deviation in an object's predicted Newtonian motion), and its slight effects become obvious in extremely strong gravitational environments, such as the immediate vicinity of Sgr A*. And only precision instruments like the VLT, which uses adaptive optics to remove the blurring effects of Earth's atmosphere from astronomical observations, can detect this deviation.
In 2018, S2 will swoop to its closest point in its orbit around Sgr A*, and astronomers using the VLT are preparing a new instrument to get an even more precise view of the extreme environment surrounding the black hole. Called GRAVITY, the instrument is installed on the VLT Interferometer, and astronomers not only predict that it will get an even more precise gauge on Einstein's general relativity, it might even detect deviations away from relativity, possibly hinting at new physics beyond relativity.