Someone inconsolable can't be comforted because they're extremely sad and despairing.
To console someone is to comfort them with kind words, hugs, or otherwise. When someone is inconsolable, they’re so upset that all the words and hugs in the world are ineffective. An inconsolable person can't be consoled. People are inconsolable after horrible things happen, like the death of a family member or a friend. Some people are inconsolable after losing their jobs or suffering disappointments. If you're depressed, you could be inconsolable. This is a strong word for extreme sadness.