A "budget briefing" is a short meeting or presentation that provides information and updates about the amount of money available and how it should be spent or allocated. Full definition
I see that preparing budget briefing materials actually comes up twice in this list, so should definitely be covered in your resume. (resume-place.com)
On Tuesday, February 11, 2014, from 10:00 a.m. to 12:30 p.m., the Fiscal Policy Institute will present its annual state budget briefing in New York City hosted by the Community Service Society of New York. (fiscalpolicy.org)
In its 28th annual New York State budget briefing book, the Fiscal Policy Institute analyzes and comments on Governor Andrew Cuomo's FY 2019 Executive Budget. (fiscalpolicy.org)