What is and is not covered under your policy can vary greatly depending upon the type of policy you have. There are very basic policy forms which only cover a list of specific perils like fire, lightning, wind, hail, etc. Other policy forms cover almost anything that is not specifically excluded.
As a general rule – there are some things that are almost never covered under a homeowners policy: Flood, earthquake damage, war, nuclear accidents, landslide/mudslide, and sinkholes. Damage from insects & vermin is often excluded, as is mold. Claims related to normal wear and tear & lack of maintenance are also usually excluded. If you’re not sure if something’s covered, it’s usually a good idea to ask your agent before you submit a claim to the insurance company.