pacify, calm, solace, gladden. Comfort, console, relieve, soothe imply assuaging sorrow, worry, discomfort, or pain. To comfort is to lessen the sadness or sorrow of someone and to strengthen by inspiring with hope and restoring a cheerful outlook: to comfort a despairing person.
Console, a more formal word, means to make grief or distress seem lighter, by means of kindness and thoughtful attentions: to console a bereaved parent.
Relieve means to lighten, lessen, or remove pain, trouble, discomfort, or hardship: to relieve a needy person.
Soothe means to pacify or calm: to soothe a child. 1, 2.