If your spouse dies without using their full exemption, you can preserve the unused amount (the "DSUE") for your own estate — but only if an estate-tax return (Form 706) is filed for the first spouse, even when no tax is owed.
Glossary · tax
Portability (of estate-tax exemption)
In plain English
A surviving spouse can inherit the unused portion of the deceased spouse's federal estate-tax exemption.