The songs speak of persistence, despair, bad luck, love, angst, and so many other common emotions. Just listen, and soon you'll be humming along as you connect to the songs.
The first song, "Free Fallin'" is, of course, a classic. In it, you can actually sense joy in Tom Petty's voice as he wails out that he's "gonna free fall out into nothing". This song is truly as American as the stereotypical girl it talks about in the opening.
Next, "I Won't Back Down" begins. I have only two words: power anthem. Oh yeah, and cheesy. However, it's cheesy in a good, 1980s sort of way.
"Love is a Long Road" and "A Face in the Crowd" are both slightly different from the previous songs in their sound, but they're equally as good. You might not be as likely to sing to them as hum, but you're probably going to enjoy them all the same. "Runnin' Down A Dream" follows them, once again embracing the persistence demonstrated in "I Won't Back Down".
The rest of the songs are great, with standouts like "Alright For Now", "Zombie Zoo", and "The Apartment Song", while "Yer So Bad" is probably the most well-known there. Give them a listen and see which ones are your favorites, as I'm positive you'll enjoy this example of classic music.