The Milky Way Backup Program (MWBP), a survey currently underway with the Dark Energy Spectroscopic Instrument (DESI) on the Nicholas U. Mayall 4 m Telescope, works at the margins of the DESI Main surveys to obtain spectra of millions of additional stars from the Gaia catalog. Efficiently utilizing times between ∼12° and 18° twilight and poor weather conditions, the MWBP extends the range of stellar sources studied to both brighter magnitudes and lower Galactic latitude and declination than the stars studied in DESI's Main Milky Way Survey. While the MWBP prioritizes candidate giant stars selected from the Gaia catalog (using color and parallax criteria), it also includes an unbiased sample of bright stars (i.e., 11.2 ≲ G < 16 mag) as well as fainter sources (to G ≲ 19 mag). As of 2025 March 1, the survey had obtained spectra of ∼7 million stars, approximately 1.2 million of which are included in the DESI Data Release 1. The DESI spectra cover the wavelength range from 3600 to 9800 Å at a resolution λ/∆λ varying from 2000 to 5000. The full survey, when completed, will cover an area of more than 21,000 deg2 and include approximately 10 million Gaia sources, roughly equal to the number of stellar spectra obtained through the DESI Main Survey, while only utilizing ≍9% of all DESI observing time. This paper provides an overview of the MWBP, describing the target selection, observing strategy, and an introduction to the resulting data.