God can't be defined
When do we hear it?
This is a common companion of "You can't prove God doesn't exist" in that postulating on the non-existence of God is a fruitless exercise. As humans we lack the capability to properly comprehend what God 'truly' is, and therefore are not competent to even define him, never mind disprove him.
The first problem with this statement is that the claim of an undefinable entity requires no refutation, so there's no point to this argument.
However the claimant is actually trying to sneak in premises. The word 'God' has a history and the entity it describes has a multitude of attributes. Furthermore, by bringing this up in response to an atheist, the claimant is also acknowledging that whatever 'God' is, exists. IN order to do that, he does have at least a working model of what 'God' is supposed to be, however nebulous, in order to have a position on the matter. Otherwise why take part in the discussion?
Here, some will claim that they have supernatural knowledge of God, enough to know He exists, but not enough to adequately define him. Even then, they need a working definition of what 'God' is, even if it's no more concrete than 'the originator of that vision/dream/inner conviction/personal witness I had'. Even so, making it supernatural is no more than an appeal to ignorance
Note: The theist who makes this claim may also posit that all 'gods' in human folklore are approximations of the 'true' god, possibly with the one tradition he favors being the closest one. In that case it is worth noting holders of the same position, but who prefer a different tradition as the closest one.