Comfort means to encourage. It comes from the Greek word, parakaleo which means “to come alongside of”. To comfort someone is to walk alongside of them during their difficulty. Sometimes, many times, it’s just being there. Words are not always necessary. Think about the times that you have been through a very, very difficult trial. You’re not looking for words or principles or theories. You just need someone. It helps to have people that you love close by.
A comforter is one who kneels down beside someone who has fallen. While it is true that God’s comfort comes from His people, sometimes it just comes down to you and Jesus. He is the source of all comfort.
For more on comfort, check out the following sections of the Bible: 2 Corinthians 1, most of the book of Psalms, especially Psalm 23, Psalm 91, Psalm 139, and 1 Peter 1.