Feeling with another.
Feeling with another — sharing or vicariously experiencing another's feelings, thoughts, and experience.
Feeling with another — actively sharing or mirroring what they feel (perspective-taking) — as distinct from sympathy (feeling for another, more distanced) and compassion (which adds a motivation to help). It implies entering into and reflecting the other's state rather than viewing it from outside, and retains technical uses in psychology and aesthetics that sympathy lacks.
Sharing in and understanding another person's emotional experience.
Now the dominant sense; Merriam-Webster notes this interpersonal use dates to the mid-20th century.
The imaginative projection of one's own feeling into an observed object.
The original sense when the word was coined — translating the aesthetics term Einfühlung.
Coined 1908–09, modeled on German Einfühlung “feeling-into” (Lotze, 1858), itself rendering Greek empatheia (en “in” + pathos “feeling”). The English coinage is credited to psychologist Edward Titchener.
A genuine 20th-century coinage. It entered English as a technical term in the theory of art appreciation (the viewer projecting feeling into an object); the now-dominant interpersonal sense — sharing another person's feelings — dates to the mid-20th century. A well-sourced shift.