If you provide incorrect information on your application, there are several things that can happen:
If the insurer finds out during the application process it can reject your application. This information may be reported to other insurers as well.
If the insurer approves your application but then finds out about the misrepresentation during the contestability period--usually the first 2 years of the policy--it can cancel the policy and return the premiums you've paid (minus any fees).
If the insurer finds out about the misrepresentation after the contestability period has ended, it can adjust your policy to match what it would have sold you originally had it known all the facts. This can take the form of a reduced death benefit, a higher premium, or both.