Someone loving is affectionate and caring. Your loving grandmother might be your favorite grandparent because she clearly adores you.
You can be a loving sister or a loving babysitter, and you can also describe kind things you do as loving, like the loving hug you give your sad friend or your uncle's loving gesture of sending your aunt flowers on her birthday. The adjective loving comes from the Old English lufian, "to love or approve," from the root lufu, "love, affection, or friendliness."