Full of deep sadness. It is a strong, serious word, and a formal or literary one — you meet it far more often in books, poems, hymns and news writing than in talk. If your friend's dog dies, you say she is 'really sad' or 'heartbroken'; you would not normally say she is 'sorrowful' unless you were writing about it. The sadness it names is the quiet, heavy, lasting kind — grief, loss, regret — not the small disappointment of a rainy day. It describes a person who feels that way ('a sorrowful widow'), but just as often the thing that SHOWS the feeling: a sorrowful face, a sorrowful voice, sorrowful eyes. It can also describe something that makes you feel that way, or is full of that feeling — a sorrowful song, a sorrowful story. Two smaller things worth noticing. First, it stretches, gently and often half-jokingly, to things that just look droopy or pitiful: 'he gave me a sorrowful look' about a boy who wants ice cream. The word is doing lighter work there, and everyone hears the wink. Second, in older and religious English it can shade toward 'causing sorrow' rather than 'feeling sorrow' — the Sorrowful Mysteries in Catholic prayer are the painful events, not sad ones. Modern learners mostly need the first meaning.