Explain why people like this movie so much

For me, there's just something about it. I was 15 and a beginner guitar player when this movie took place. So I identify quite well with the era.
When I compare this to that other great 'band' movie - Almost Famous (a better movie), I think that was a movie about being 'with' the band. TTYD is being IN the band. Just like my youth. And I was in a touring dance band in my 30's, so I get that part, too. Meeting and hanging out with other bands and people.
ALL the songs are great, by all the bands. As are the characters. (and I love the reveals in the director's cut!)
Like Breaking Away (I also raced bicycles in my teens), these movies were just made for me. But, not for everyone. There may be a hundred similar storylines, but this one sings to me!
And for those who like Steve Zahn (like me), watch Ethan (TBP) more closely. He's always doing something, small and clever. The other two big standouts are Del Paxton and Lamarr at the hotel. Just perfect!
But to answer your question, I guess it's like asking why people liked the Beatles, or Fountains of Wayne (who sang the theme?), or any other band. Or RAP! That would be un-explainable to my generation!

Why do you ask? You have no soul, and people who enjoy this movie do. How can a one explain a happy, merry and great yet not to take seriously movie with a great storyline to base it on. Your the walking dead. You need to eat brains thats why you dont get it.

I like it because it's a sweet feel good movie without being syrupy. All of the characters motivations make sense and it has lots of memorable scenes which feel unique to this movie...,so it feels real.

Take for example when wolfman is brought in to play....as viewers we know that the band needs a replacement for the bass player....even if the band doesn't know it yet....then wolfman plays his riff and impresses the band and us the viewer....and the band walks away humbled....nothing belabored....point made. Makes for an enjoyable scene...like many others.

It's one of the most well-made films ever made. The script is tight--there is no fat, no filler, every single thing is set up and has a pay off, it's smooth, it's seamless, so you don't even notice it, which is another reason you can watch it over and over, you see new things every time.

In the beginning when Guy is introduced, Lenny makes it clear they were in a band together before, so the audience knows Guy is a drummer. When they need a drummer and they go to Guy, it seems natural. The base player is doing push ups before their first big show in Pittsburgh (so when he later drops and does them in the coffee shop, it makes sense). The whole movie is like that. Brilliant script in terms of craft.

Uproxx recently did an article about the movie, called "We should be talking more about That Thing You Do. Check it out:
http://uproxx.com/movies/2015/08/that-thing-you-do/
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The ensemble chemistry is great, the Beatles' story parallels, good music, beautifully acted, extremely well put together, lovable characters (the band, Guy's family, etc.), and the reunion of Peter Scolari and Tom Hanks. What's not to love?