This sentence introduces the account of Terah's descendants. It could be translated as "This is the account of Terah" or "This is the account of Terah's descendants." Genesis 11:27-25:11 tells about Terah's descendants, particularly his son Abraham.
This means that Haran died while his father was still living. It may also be translated as "Haran died while his father, Terah, was with him" or "Haran died while his father, Terah, was still living."