The expression "to know" is found in the King James Version at Genesis 4:1:
And Adam knew Eve his wife and she conceived and bare Cain
The New International Version translates the Hebrew text this way:
Adam lay with his wife and she became pregnant and gave birth to Cain
Clearly, in this instance, "to know" refers to sexual relations between a man and a woman resulting in procreation.
There is another instance (in Genesis 19:5) where the King James Version uses the expression "know". It's when the men of Sodom wanted Lot to bring out the two men (angels of the Lord) who were staying with him:
Bring them out to us, that we may know them
The NIV is more specific:
Bring them out to us so that we can have sex with them
In the Old Testament, the Hebrew word "yadha" is translated as "to know" in the King James Bible in Genesis 4:1, and within the context of that verse it is a euphemism for having sexual relations.
The Hebrew word in Genesis 19:5 may have been "shakhabh" which is a reference to homosexual sex. The King James Version may have deliberately chosen to use a more "delicate" English word (know) in order not to offend the sensibilities of the 17th century readers.
In the New Testament, there are Greek words which can be translated as "know" but in the intellectual, and not physical, sense. I hope that helps.