In 1998, Hubble was pointed at the nearby star HR 8799. At 130 light years away, it's one of a group of young stars that were suspected to have planets. Despite the best efforts of the astronomers involved, though, no planets were discovered.
Fast forward ten years. In 2008, planets were indeed found orbiting HR 8799. Those observations, using the ginormous Gemini 8-meter telescope, were among the first exoplanets directly imaged (as opposed to inferred using indirect techniques), and they made up the first exoplanet solar system ever directly seen.
Armed with this knowledge, in 2011 astronomers went back and looked once again at the 1998 Hubble data. Using sophisticated techniques and data unavailable 13 years ago, they were able to painstakingly subtract the light from the star, removing its glare, and revealing the planets as seen in the image above. In a sense, this image was the very first one to ever directly show exoplanets, but in reality that's not entirely fair.
Still, it's an incredibly important image: it gave us an extra 13 year baseline in observing these planets, long enough to actually detect their orbital motion around their star! The three planets seen take 100, 200, and 400 years to orbit once, so even these few years of extra data have helped astronomers understand better planets orbiting another star, over a thousand trillion kilometers away.
Image credit: NASA, ESA, and R. Soummer (STScI)