Music today often has a lot of artists making use of parts of other artist's songs. There's nothing wrong with it - just as long as you get the OK from the artist and his record company and make a deal to share a piece of the profits. Sometimes it just happens without all the legal stuff, but it's usually when a popular song gets "sampled" by someone else trying to make a name for themselves (anybody remember Ice Ice Baby by Vanilla Ice?)
In this case, it's a Christian rapper called "Flame," who's not exactly a household name, who insists that Katy Perry ripped off a 16 second piece of his song "Joyful Noise." The rapper sued Katy for $20 million (the song made $41 million), and the jury in the case bought the rapper's argument, but awarded him the paltry sum of $2.78 million. Katy is to pay $550,000 and Capitol Records (her label) will pay the rest.
Videos from both songs are posted here, so listen to each and see if you can hear the similarities. While you're doing that, you can also ponder how a mega-star like Katy with a extremely successful producer would have come across a Christian rap song and decided to just rip it off? There are plenty of dishonest people in the music business for sure, but this has never seemed like one of those times.