Our explanation of the term "the ineffable God" is necessarily a matter of theology and not language. An acceptable explanation has to be theologically sound.
Without going into the detailed theology of it, we can explain this word "ineffable" when applied to God thus: God transcends all human language and no humam word or name can be an adequate name for God. We cannot speak his name because he does not have one in any human language. This is what is meant by the ineffable God or the ineffable name of God.
(For those whoare interested in the theology, here is a start. The name God gives to Moses, "I Am Who I Am" (Ex 3:14), is a revelation, but it is also ineffable and incomprehensible to the very limited human mind.)