What does it mean to play a piece with "feeling"?
Someone asked me this question recently, and I think it's a GREAT question. It's maybe the ultimate question, because it bring up so much more than is just on the surface.
I think most musicians have asked themselves this at some point in their lives. For me, the real value of the question is that it's a lifelong study.
Some musicians get feeling from the pieces they play. A Mozart slow movement might evoke a tenderness which the performer feels and then tries to bring out even more while playing the music. And it's not tied to any particular genre! Classical music, rock and roll, jazz, and even hip hop can all evoke anything from tenderness to joy and elation.
Other performers bring their own feelings to the music. We all know singers, pianists, and other instrumentalists who tend to "brood," or smile, or whatever. They bring their natural emotional state to the music as a whole. Tony Bennett, for example, tends to sing in a positive, happy way, while Frank Sinatra alternated between forceful and sensitive. In jazz piano, Art Tatum played was an extrovert while Bill Evans was more introspective.
Still others focus more on musical dynamics, etc., and let the piece speak for itself.
Studio and backup musicians are like this, since they have to adapt to whatever is asked of them at the time. A keyboard player might play one way for Beyoncé and quite another way for Taylor Swift.
What's your approach?
If you absorb everything you can about music, and then continually investigate the subject of musical feeling while you're practicing and playing, you're sure to have a long, richly rewarding involvement with music. (And yes, there will be moments of deep and profound feeling!)
Enjoy your music. It will take you to places you don't yet know exist.