This expression is used to make someone understand that they should accept a criticism because, deep down, it's correct

“I overheard Clara complaining because I'm always in a crappy mood and I treat her like dirt” “Well, if the shoe fits…”

“Ho sentito Clara lamentarsi perché dice che ho un carattere di merda e la tratto come una pezza da piedi” “Chi ha orecchi per intendere, intenda!”

“Stop telling me that! I got it! Do you think I'm an idiot?” “If the shoe fits…”

“Basta, non ripetermelo più! Ho capito! Mi credi un idiota?” “A buon intenditor…”

"It's a difficult problem in a difficult situation, and many people would seek help from an expert" "Are you telling me that I'm not able to do this?" "If the shoe fits..."

“È un problema difficile in una situazione altrettanto difficile e molti chiederebbero aiuto a un esperto” “Mi stai dicendo che non sono in grado di farlo?” “A buon intenditor…”

Short of the original phrase “If the shoe fits, wear it.”
This saying is the American adaptation of the older British proverb "If the cap fits, wear it." This line was in 1705 in a satirical poem - critical of the British parliament - by Daniel Defoe and said: "Gentlemen, and if the Cap fits any Body let 'em wear it."
The change from cap to shoe may well have been influenced by the Cinderella story, which has a tight-fitting slipper as the primary plot device. After Giambattista Basile released, in 1634, Il Pentamerone, a well-known collection of Italian folktales, versions of the story with the "lost slipper" scenario were well known by 1773 in both Europe and the United States. One of those stories, Cenerentola, is the basis for the contemporary Cinderella story, complete with ugly sisters, a wicked stepmother and a lost slipper.