This idiom is used when we mean that we cannot understand someone or something at all, that is, we cannot make any sense of someone or something.
It may also be used in plural: “Make heads or tails (out) of it”, but this form is more frequently used in the US.
- I’ve been working with this program for hours, but I still can’t make heads or tails (out) of it.
- Kevin is so strange. I can’t make head or tail of him.