Conclusion

This is the expected conclusion that you are hoping the court will agree with.  It shows what your argument is going to attempt to back.

Rule

The rule is highlighting important statutes, decisions in other cases, and other legal authorities to create a set of rules that are applicable to your argument.  These will be referred to throughout the argument and used as a baseline that the argument must work around.

Application

This is where the argument is made.  This section uses facts from the case and presents them persuasively to back the conclusion that was highlighted at the beginning of the argument.  This is often presented as a series of facts and pieces of evidence followed by an explanation of how they apply to the case and why they back the conclusion they want the court to agree with.

Conclusion

Restates the initial conclusion to remind the court of the conclusion they should draw now that they have the evidence and reasoning to support it.