If you have a criminal conviction, then you might find it hard to get accepted for some types of insurance, or may be charged higher rates when you declare your circumstances. If you, for example, have a motoring conviction, then a car insurance company may opt not to give you a quote, may charge you a higher premium or may add exclusions to coverage because you pose a greater risk.
This can apply to you, people who live in your household or people named on policies. Not all insurers will ask about convictions during the application stages, however, and many people do not realise that they should disclose them. This can also lead to problems in the future, if the information then comes to light, and cover can be invalidated or cancelled.