A sound financial system is essential to promote economic growth because financial systems allow for the lending and borrowing that promote growth.
Without a sound financial system, two negative things happen. First, people stop saving their money in lending institutions. If, for example, you do not trust the banks, you do not put your money in them. Second, lending ceases. If people will not deposit money, banks will not be able to lend. If banks and other financial institutions do not lend out money, businesses cannot start or grow. This was a major problem that occurred after the crash of 2008. Banks stopped lending (in this case because they were afraid of losing their money making bad loans) and the economy sputtered because businesses had a very hard time getting the money they needed.
Therefore, a sound financial system is essential so that money can be lent and borrowed and businesses can grow, thus causing economic growth.