The limelight means the centre or focus of attention. If you are in the limelight, you receive the attention and interest from the public. In Spanish we say “Ser el centro de atención, estar de actualidad”.
You will probably agree with me that these children who burst in on their dad, Professor Robert Kelly, while being interviewed by the BBC are a clear example of this expression, taking into account that the video went viral.
These charming kids steal the limelight once more, as they will feature a cartoon trying to help their father out with his important UN jobs. You can read the news here: http://www.bbc.com/news/world-asia-39724383