The little information they've received thus far points to "an unexpected mismatch between camera software and data-processing software in the main computer", though they'll know more after a full data dump. It will take some time to draw information across the gulf of space between Mars and Earth, which were only 46.8 million miles away from each other at the end of May. Curiosity can transmit data directly back to us or relay it through the Mars Reconnaissance Orbiter to relay homeward at varying data transmission rates depending external conditions.
This likely isn't a big deal: Curiosity has put itself into precautionary safe mode before, in three separate incidents in 2013. In one, a memory glitch put it out of commission before NASA restored its systems from a backup. This shutdown could be a bit of robot protest after the space agency put off the rover's retirement last week, extending its mission an additional two years starting October 1st, 2016. There's more frontier geology to explore and possible water to sample before Curiosity gets its deserved rest.