Palma vs. palmo
Both the Italian words palma and palmo can be used to translate the English word "palm" when referring to the hand. While they describe the identical part of the body, they differ in grammatical gender, their frequency in everyday conversational language, and their use in specific idiomatic expressions.
Palma
The feminine noun palma refers to the anatomical inner surface of the hand. Because the word palma is identical to the Italian word for "palm tree", it is almost always paired with the clarification "della mano" (of the hand) when used in this context. It is widely used in descriptive, medical, anatomical, or formal contexts.
Il medico ha esaminato la ferita sulla palma della mano.
(The doctor examined the wound on the palm of the hand.)
La chiromante legge le linee sulla palma della mano per prevedere il futuro.
(The fortune teller reads the lines on the palm of the hand to predict the future.)
Sentiva un fastidioso prurito nella palma della mano sinistra.
(He felt an annoying itch in the palm of his left hand.)
Appoggiò la palma della mano sul vetro freddo della finestra.
(She rested the palm of her hand on the cold glass of the window.)
Il bambino si è sbucciato la palma cadendo dall'altalena.
(The child scraped his palm falling from the swing.)
Palmo
The masculine noun palmo strictly means the palm of the hand and is the preferred term in everyday conversational language. It does not share its meaning with a tree, so it is clearly understood even without adding "della mano" (of the hand). Furthermore, palmo is extensively used in standard Italian idioms and historically refers to an ancient unit of measurement similar to a hand's breadth.
Scrisse velocemente il numero di telefono nel palmo.
(He quickly wrote the phone number on his palm.)
La bambina stringeva una moneta nel palmo destro.
(The little girl was squeezing a coin in her right palm.)
I poliziotti ispezionarono la scena del crimine palmo a palmo.
(The police officers inspected the crime scene inch by inch.)
Tutti sanno che la nonna tiene il nipote in palmo di mano.
(Everyone knows that the grandmother holds her grandson in high esteem.)
Dopo aver perso l'opportunità, è rimasto con un palmo di naso.
(After losing the opportunity, he was left feeling deeply disappointed.)
Versa un po' di bagnoschiuma nel palmo e strofina bene.
(Pour a little body wash into your palm and rub well.)
Summary
To summarize, use the feminine palma (usually as palma della mano) when referring specifically to the anatomical flat surface of the hand, keeping in mind its dual meaning as a tree. Use the masculine palmo for direct, everyday conversational references to the hand's palm, as well as when utilizing common idioms or spatial measurements.