Bottom line: Parents moved by faith act to "save" their family.
Heb. 11:7 shows us that Noah was a believer (a parent) that was moved by his faith to trust God's message about the future, act on what he believed, build an ark and ultimately save his family from future judgement and death and from the wickedness and spiritual dangers of the culture in which he lived.
We can learn from Noah's example that we too can by faith "save" our family.