They were studying plasma, which is the state of matter that makes up most things in the universe (though only visible in a few things, like lightning strikes and the gas inside neon signs, on Earth). Plasma is basically a gas that's been charged with enough energy to loose electrons from the atoms holding them. The net charge of a plasma is still neutral, but it's full of negatively charged electrons and the (now positively charged) ions they've ditched, which gives it some weird properties. I'll allow They Might Be Giants to explain further:
When the researchers in the new paper shot high-intensity lasers at plasma (as people studying plasma are wont to do) they noticed that the impact was leading to the production of a sound wave: In the instant after a laser strike, plasma would flow in a way that led to a kind of plasma traffic jam, and the pressure would create sound pulses.
"One of the few locations in nature where we believe this effect would occur is at the surface of stars," study author John Pasley of the York Plasma Institute said in a statement. "When they are accumulating new material stars could generate sound in a very similar manner to that which we observed in the laboratory -- so the stars might be singing -- but, since sound cannot propagate through the vacuum of space, no-one can hear them."
Because sound travels from one vibrating molecule to another, it can't technically move through space -- there aren't molecules there to bounce against each other and pass sound waves along. But wait, you say, NASA has recorded space sounds! Those are actually made by converting other kinds of waves and energy into sound waves. If you somehow managed to withstand the heat and lack of oxygen of an active star and sat right next to it, you wouldn't hear a peep it made.
Even if those whines had a way of traveling through space, we wouldn't be hearing a stellar symphony. These sounds are so high frequency -- around a trillion hertz -- that it's pretty certain nothing would hear them. That frequency is 6 million times higher than anything any mammal can hear. It would even blow past the hearing abilities of moths, some of nature's best squeaky-sound-listeners, who can manage about 300,000 hertz. But it's definitely fun to think about what stars might be doing beyond the boundaries of our perception.