Ineffably means in a way that is too great, too beautiful, or too deep to put into words. You use it to dress a feeling or a quality: someone is ineffably kind, a place is ineffably sad, a moment is ineffably strange. It is the adverb of ineffable, and it has the same literary, slightly old-fashioned colour. You will not hear it much in the street; it belongs to careful writing and to people who like a high, soft tone. Though actually, some speakers use it just as a fancy 'very' or 'amazingly', which is a looser, lighter use than the old religious and poetic one.