A tender-hearted person feels other people's pain easily and is soft in how they treat others. They cry at films, cannot watch an animal be hurt, give money away, forgive the person who wronged them. The word points at the softness inside — the heart itself is soft — rather than at what the person does, so it names a nature rather than an action. It is warm and affectionate in tone, and slightly old-fashioned; you meet it often in novels, in church language, and in the way older people describe a grandchild or a gentle son. Younger speakers today are more likely to say 'soft-hearted', 'a big softie', or 'so sweet'. There is a small shadow inside the word that students often miss. Because being tender-hearted means being easily moved, it can carry a light hint that the person is a bit too easily moved — too soft to say no, too soft for a hard job. 'He is too tender-hearted to fire anyone.' That is affectionate teasing, not an insult, but the tilt is there. Notice too that it is almost always used before a noun or after 'be': 'a tender-hearted woman', 'she is very tender-hearted'. Keep the hyphen when it sits before the noun.