What exactly is hypothyroid? And is it hereditary, if I give birth can my child have it?

Low risk for child. Hypothyroidism is fairly common and can run in families, especially those that have a tendency to have autoimmune diseases, one of which is hashimoto's thyroiditis. Children very rarely get this. We are beginning to find some gene changes for many autoimmune diseases, but the influences are small and the genetic tests are under development. All newborns are screened immediately for hypothyroidism.
Underactive thyroid. Hypothyroidism describes an underactive thyroid. Thyroid hormones control metabolism and affect almost all organs in the body. There are different causes for it but hashimoto's thyroid disease (autoimmune) is the most common one. It runs in the family. It needs to be diagnosed and treated if you are trying to conceive or during pregnancy. It can be diagnosed on a blood test.