When you are refused insurance it means that the provider has decided not to provide cover for your property or belongings. This may be because you do not meet the terms of their underwriters, or it may be because of a change in your circumstances which means you are perceived to be a greater risk to insure.
When applying for insurance, if you do not, when asked, tell your insurer something that is relevant such as having a criminal conviction, then you could be refused house insurance.