To wish very strongly, especially for something that you cannot have or something that is very difficult to have: (Cambridge Dictionary)
To long persistently, wistfully, or sadly. (Merriam – Webster)
To feel tenderness or compassion. (Merriam – Webster)
If someone yearns for something that they are unlikely to get, they want it very much. (Collins Dictionary)
Have an intense feeling of longing for something, typically something that one has lost or been separated from. (Oxford Dictionaries)
Examples
Yearns for chocolate.

https://www.flickr.com/photos/gerrythomasen/15009036079
Yearn song, Chuck Perrin.

http://chuckperrin.com/albums/the-yearn/