Tenderness is a feeling of concern, gentle affection, or warmth. It's the quality of a person who cries when they see someone get hurt or who gently picks up a tiny kitten.
Writing a heartfelt note to a sad friend is one way to show tenderness, and so is giving your brother a sincere hug on his birthday. Another definition of this adjective is "extreme sensitivity to pain." You might experience tenderness in your muscles the day after going on a long hike. This is actually the original meaning, from tender, "soft or easily injured," and a root meaning "stretched, thin, or weak."