Both refer to things that continue without stopping. Continual is used for things that happen repeatedly, or for things that are annoying. Continuous is used for things that go on without interruption.
There were two weeks of continual rain last month. Her boss didn’t want to listen to her continual complaints. His continual attempts to improve the relationship have failed.
We had three continuous hours of English class. On this 24-hour news channel there’s a continuous flow of information. There has been a continuous fall of unemployment since 2010.