Solicitude is more-than-average concern for someone. When you're sick in bed, it's nice to have someone around to treat you with solicitude, hovering nearby, bringing you cups of tea, and handing you tissues all day.
Someone who shows you solicitude obviously cares about you. You could act with solicitude toward a lost child in a shopping mall if you calm him, dry his tears, and help him find his mother. Sometimes solicitude implies too much concern, bordering on anxiety. The Latin word for agitated is sollicitus — which is also the root of solicitude.