1) Too great, too wonderful to be expressed or described in mere words. An indescribable feeling, person or thing that exists only in fleeting thoughts.
2) A term used by an angel to describe the Plan of God; Her Ineffable Plan. Separate from the Great Plan.
Anything ineffable is unspeakably beautiful, moving, or horrible. It's beyond expression. If something is so powerful or emotional that you can't even describe it, it's ineffable. Ineffable ideas and emotions are difficult to put into words.