It's just like "move" or "touch" in English.
e.g.我被感动了。 I was moved/touched.
(If something moves you, it has an effect on your emotions and causes you to feel sadness or sympathy for another person.)
(If something that someone says or does touches you, it affects you emotionally, often because you see that they are suffering a lot or that they are being very kind.)
- The Oxford Dictionary & The Collins Dictionary