Rather than just post the audio of the song, this is a video of it, along with the last several minutes of the show. It's comes from the Roundabout Theatre production in 1983 that starred Judy Kuhn and Boyd Gaines.
She Loves Me is based on the Hungarian play (and its subsequent Hollywood movie, Shop Around the Corner) which were the foundation of the movie You've Got Mail. If you've seen any of those, you'll have a good idea of what's going on in the sequence here. During the course of the song, the young man, Mr. Novak, tries to build up his relationship with Amelia Balish, with whom he had long been sniping, but only recently discovered has been his pen pal with who he's in love.
The video jumps from this to the finale, when Miss Balish at last realizes he has long been her secret pen pal who she's in love with, as well. (The line he sings, to prove who he is, "I am so sorry about last night," is the first line in the letter she wrote to her pen pal, apologizing for the screw-up when they were supposed to have met at a restaurant.) And it all leads to a reprise of the wonderful song, "Ice Cream," with new lyrics for the occasion -- and then into the curtain call.