I would appreciate if someone could explain the meaning of the phrase "I have but one claim to fame". I understand every separate word, but the meaning of the whole phrase is fairly obscure to me, as I am not a native speaker.
Let's break this down into simpler parts:
In other words, the declaration is equivalent to "There is only one reason that I have become famous."
The phrase "claim to fame" is commonly used to describe something noteworthy of an otherwise unnoteworthy person.
It can be used in a literal manner, describing an actual accomplishment made by a person that really has made them famous. For example, Captain Chesley "Sully" Sullenberger's claim to fame was his successful landing of US Airways Flight 1549 in the Hudson River off Manhattan, New York. This incident was Capt. Sully's claim to fame because before the successful crash landing he was a virtual unknown, but afterwards he wrote a book, appeared on several television and radio talk shows, and so on.
More commonly, the phrase is used tongue-in-cheek to note a unique talent or ability, regardless of whether said talent or ability makes you actually famous. If your neighbor could recite by memory all of the poems of Edgar Allen Poe, you could say that was his claim to fame.
The phrase, "one claim to fame" usually means that the person has a single claim to fame. If you say, "Bob's one claim to fame was that he could ride a unicycle while singing the national anthem," that implies that Bob has but one unique talent. But, when speaking of Bob you might say, "One claim to fame is that he can ride a unicycle while singing the national anthem." In this usage it's unclear if riding a unicycle while singing the national anthem is Bob's sole claim to fame or if it's just one of Bob's claims to fame.