That question is tricky- how do you know you love a song in a musical? The songs are KEY to any musical. They form the backbones to the characters and plot. All the songs have to sound like they fit into the musical itself, but you STILL have to love the songs. You can’t love a musical without loving the songs first.
Well- a lot of time, for me, I usually JUST know. What do you mean, YOU JUST KNOW. That literally means you are into the songs automatically- BEFORE the lyrics and before the dance/spectacle element.
This is another section- did you form an emotional response? That can mean anything like feeling like you are hit like a pile of bricks (tears or choked up or feeling like you want to, but just can’t get it out- one of those does happen when “getting hit like a pile of bricks” feels like). That emotional response also drives you to stay at the edge of your seat. Your emotional response is not ALWAYS hit like a pile of bricks- the songs could make you want to root for the characters. Did the songs make you vulnerable? That list can go on- the emotional response is pretty much the same thing as emotional connection.
The emotional pull to the songs start to make us care about the characters and their storyline. I do not think there is a musical genre that is better at storyline than musical theatre. The closest that I can think of is Opera, which is also a genre of storytelling.