‘And Jacob kissed Rachel and lifted up his voice and wept. And Jacob told Rachel that he was her father's brother and that he was Rebekah's son. And she ran and told her father.'
The meeting is emotional. In days when families were often out of touch for years such scenes were a regular feature of life when they came together. It must be considered certain that Jacob had said something introductory before he kissed Rachel, something like “I am your cousin'. He has after all gone to great trouble to water her sheep and this would hardly be done without saying anything. But after his rapturous welcome he then explains his relationship in more detail. Then, quite excited for she will have heard of her wider family, Rachel runs to tell her father.
“Her father” s brother', that is, a blood relation, his ‘kinsman'. Strictly he was his nephew. The word for ‘brother' had a variety of meanings, compare Genesis 29:4.