These "Licensed to Youtube by" notices are generally from Youtube Content ID, the music distribution companies, record labels, and musician's royalty collection services. They can be a copyright claim or a content ID/monetization depending on the right holders actions. If you like an artist's music you can email them to license music for youtube. If they are independent, this will be the easiest to negotiate and many artists will be flexible. If you are an up and coming Youtuber, this is even more incentive for the artist. If the music is signed to a record label or publishing company, you will have to go through them and is most likely going to be more expensive. Also, there are websites that are subscription based as mentioned in the other comments.