Honours is one way to do 400-level study after one has completed a Bachelor's degree, the other ways being the Postgraduate Diploma or a Master's degree.
To be eligible for an Honours degree in Computer Science at Otago, a graduate needs to have majored in Computer Science, to have included COSC341 or its equivalent, to have achieved at least a B+ grade at 300-level, and to have completed at least five 300-level papers.
During the Honours year, one is required to include the COSC490 research project plus four 400-level COSC papers. The COSC490 research project has to be research-focused and is thus more constrained than the COSC480 project.
If you are considering Honours, your first step should be to consult the adviser of studies.