The Bible does not say much about Terah, but we can put together some of his life by looking at the text in Genesis 11 and the genealogy Luke provides in his Gospel.
Terah was the father of Abram, who later became Abraham. When we first see him mentioned in the Bible, he resided in the city of Ur of the Chaldean Empire.
Family
We do not know his early life. However, we do know that he was part of the line of Shem, and his father's name was Nahor.
He would have had multiple wives, and many more children are mentioned in Genesis 11:27 - 12:9.
We know this because Abram married his half-sister Sarai. This is not mentioned until later when Abram is traveling to Canaan. Terah also lived until he was 205 years old, and it was not uncommon to have children later in life due to the longer life spans.
The men who are mentioned are his three sons: Abram, Nahor, and Haran.
Haran was the father of Lot and died young, which left Lot with Abram as a young boy.
Nahor's significance is that he married and had other children, while Abram married and did not have any with Sarai.
Religion
It is assumed that Terah and his family worshipped the false gods of their native land.
This would mean that God called Abram to himself when Abram was not seeking after him and was, in fact, involved in a false religion.
There is a possibility that Terah converted to Abram's belief in God since Abram was called by God prior to, and the two traveled with each other until his death. However, the Bible never says anything about his religion or possible conversion, so one can only make assumptions.
Wealth
It is clear that Abram was a man of wealth, and it can be assumed that his father had some wealth, too. However, the Bible emphasizes how wealthy Abram became, so it is clear that Abram's wealth would dwarf that of anyone in his family.