Cool stuff.....
OK so what that means is they want to know what known/popular artists already out there have music that is of a similar nature to what you have written.
Film people, video production companies, and artists will contact the publisher and say that they want a song that sounds like such and such an artist. The publisher does a search of their database and looks for "sounds like" that artist and complies a list for the end user. Licensing the original recording artist could cost upwards of tens of thousands of dollars, but they can license a "sounds like" song for a couple hundred. So you do need to do some research and perhaps have some friends who are knowledgeable about music and artists give you an honest assessment of the songs from a "sounds like" perspective.
The first song you and I ever did.... September Nights, when I played this for my wife, her comment was.... " that sounds like Layla by Eric Clapton.. in a way"..... waa laa, there's your "sounds like".... Above the Clouds was one that I wrote and you played on that sounds like the theme song in a movie I started to watch.....
It might take a friend with a good ear.... or some research and listening to music on your end. You could always post the songs and have people here do the work for you..... there are some pretty diverse musical taste's here. I'm sure the folks here could nail a few of them for you in short order.
You see this happen a lot... someone posts a song and people comment .... wow that sounds like a Bob Dylan song or some other artist. That's the feedback you want.
As far as the publishers and libraries, it is pretty important that you get this correct. That way your music gets categorized into the correct areas and people seeking "sounds like" can find it. If you have a great song that is in the wrong category, no one will find it and it will end up never being used.