'briefly explain' is correct and usable in written English. You can use it when you want to ask someone to provide a concise description of something. For example: "Can you briefly explain how the new software works?".
Briefly explain.
Let me briefly explain.
Let me briefly explain our role.
AHRENS: May I briefly explain this sketch to you?
And I shall briefly explain why this is so.
I'll briefly explain the basics of both here.
Below, a complicated graphic that I'll briefly explain.
Make a list and briefly explain why each is important.
List these and briefly explain why you choose them.
Allow me to briefly explain the tantalising plot.
First we briefly explain our view on phonology and phonetics.
Awesome tool! I started using it one year ago and I never had to look for another app
Ha Thuy Vy
MA of Applied Linguistic, Maquarie University, Australia