To touch someone to the core.
To touch someone to the core — to set off a sudden swell of feeling (tenderness, pity, warmth) strong enough to bring tears. Reflexively, commuoversi is to well up; the state itself is the noun commozione.
Names the event of being emotionally stirred — of which tenderness may be one trigger — rather than a sustained state. Unlike catharsis it implies no purgation, just the welling-up of feeling itself; unlike compassion (sustained fellow-feeling for suffering), it is a momentary being-moved that beauty, kindness, or joy can trigger as much as sorrow (“il film mi ha commosso”).
com- (intensive) + movere “to move” = “to thoroughly move.”
From Latin commovēre “to set in motion, agitate, move (emotionally),” com- + movēre “to move.”
Inherited the Latin range from literal “set in motion / agitate” (still in literary use) through “incite to revolt” to the now-dominant figurative “to move deeply.”
Popularized in untranslatability lists as uniquely “to be moved to tears by a story” — this overstates it; it closely parallels English “to be moved,” and is an everyday verb. Precision: commuovere is the verb; the emotion-noun is commozione.