My Finest Hour

"When my words came stumbling out then I went tumbling out"

To me, these words signify the nervous babbling which can expose someone's vulnerability. Just something I relate to lol.

Her voice is just amazing.

Seems like a story of a person that fell deeply in love with someone that was a bit too dangerous for their comfort. They were madly in love with the person despite that, but because of their fears, they passed on what would have been the most amazing experience of their entire life. It would have been (and it secretly was) the highest point in the person's life to be in love with the dangerous person.

The singer still sees this person from time to time. It seems as though she is still friends with this person and that they still share a very special bond that others do not know or understand. But even when she is in this person's company, she is still reminded of how very different they are and she immediately wants to cling to comfort again (I'm going home).

But then she again argues with her own heart about whether she should have been with this person or not, vacillating between this person being "the one"("should've been you") and this person being the wrong person for her ("you're too young") which suggests she felt this person was not quite mature enough for her.

Just one girl's interpretation. Not sure if it's right!

This song is about someone thinking back with pain and regret on what might be the lowest point in her life, and gradually coming to terms with it. Thus, the title “My Finest Hour” is ironic. Her low point comes about following her ill-advised attempt to connect romantically with an older, more experienced and accomplished man, one who likes afternoon tea, poetry, and corresponding by mail the old-fashioned way. Perhaps he is her English literature professor at university where she is a student.
The song begins with her feeling of defeat, or being "shown up", by circumstances ("When the world it shows me up...."). She irrationally blames her youthful age, as reflected by the way she dresses as she normally would for her stage in life, in contrast to the man who is the object of her admiration ("My clothes they show me up....") She berates herself as naive, lacking in enough self-awareness ("...I never knew this before....") or experience ("...I've never been hit before...") to have foreseen this turn of events.
She bitterly recalls an anecdote she had blurted to him uncontrollably, using "words" that came "stumbling out", about how she luckily came upon a coin in the London subway station. ("The finest hour that I've ever known / Was finding a pound on the Underground....") Bitterly and sardonically, she calls that her "finest hour" she's ever known. In retrospect she feels that telling him that story had backfired on her by emphasizing their age difference, despite her intention to avoid doing so.
She had been repeatedly but unsuccessfully trying to form a relationship with him, dreaming that they might be soul mates ("And I keep hoping you are the same as me…”), by writing him letters and coming over to his place for tea and discussions of poetry. She realizes that a romantic relationship between them would be considered inappropriate, but was willing to rebel against societal rules to pursue him ("We are who we are, what do the others know...." and "...whatever the others say....") She even fantasizes about trying to use illegal means to legitimize her idea of a romantic relationship between them ("Bribed the judge and sat down....") Eventually she confesses that that it's not poetry that interests her and it was just an excuse to spend time with him ("...poetry is not for me....") She has no clue how to develop their platonic, mentor-mentee relationship into something intimate, so she asks him to show her how. ("...so show me the way to go....") He rejects her as "too young". In the line "Show me the way to go... (home)", the “(home)” parenthetical represents his reply to her question by telling her to leave. She goes "tumbling out" of his residence, mortified, perhaps in tears, returning to her dorm room for solace. ("Oh, I'm going home...." and “Oh, I just want to go home…”) The refrain of “You’re too young….” In the final section represents his words of rejection echoing in her mind as she dashes mortified from his place, intertwined with her heart's regret at the notion that he could have been the one for her ("Should've been you....). In her mind, their words and her thoughts merge and overlap ("Should've been you...you're too young...bribed the judge and sat down...").
It ends with the repeated phrase "you're too young", meaning that she is starting to accept that it would not work out between them.