An advance VAT return (Umsatzsteuervoranmeldung or UStVA) is a monthly or quarterly VAT report.
It’s called an advance VAT return because you report your VAT in advance of your yearly VAT declaration (Umsatzsteuererklärung).
It tells the Finanzamt how much VAT you charged your customers, and how much VAT you paid your suppliers. You must give the difference to the Finanzamt.
For example:
You made 20,000€ in sales, including 3,193€ VAT
You paid 12,000€ for tools and supplies, including 1,916€ VAT
You must give 1,277€ to the Finanzamt (3,193€ − 1,916€)