What could brown spots on my neck and shoulders signify?

Many Things. Any skin condition requires visualization in order to properly diagnose and treat. Without seeing it, some ideas are that it could be freckles, or sun spots. Also, there is a particular skin fungus called tinea versicolor that can leave light or dark spots on the skin commonly on upper body. A little more information is needed. Have a dermatologist take a look.
Many causes. These lesions need to be visualized & a history needs to be obtained in order to make an accurate diagnosis. Sometimes lab testing or biopsy is necessary.