We describe the survey design and science goals for One-hundred-deg(2) DECam Imaging in Narrowbands (ODIN), a NOIRLab survey using the Dark Energy Camera (DECam) to obtain deep (AB similar to 25.7) narrowband images over an unprecedented area of sky. The three custom-built narrowband filters, N419, N501, and N673, have central wavelengths of 419, 501, and 673 nm and respective FWHM of 7.5, 7.6, and 10.0 nm, corresponding to Ly alpha at z = 2.4, 3.1, and 4.5 and cosmic times of 2.8, 2.1, and 1.4 Gyr, respectively. When combined with even deeper, public broadband data from the Hyper Suprime-Cam, DECam, and in the future, the Legacy Survey of Space and Time, the ODIN narrowband images will enable the selection of over 100,000 Ly alpha-emitting (LAE) galaxies at these epochs. ODIN-selected LAEs will identify protoclusters as galaxy overdensities, and the deep narrowband images enable detection of highly extended Ly alpha blobs (LABs). Primary science goals include measuring the clustering strength and dark matter halo connection of LAEs, LABs, and protoclusters, and their respective relationship to filaments in the cosmic web. The three epochs allow for the redshift evolution of these properties to be determined during the period known as Cosmic Noon, where star formation was at its peak. The narrowband filter wavelengths are designed to enable interloper rejection and further scientific studies by revealing [O II] and [O III] at z = 0.34, Ly alpha and He II 1640 at z = 3.1, and Lyman continuum plus Ly alpha at z = 4.5. Ancillary science includes similar studies of the lower-redshift emission-line galaxy samples and investigations of nearby star-forming galaxies resolved into numerous [O III] and [S II] emitting regions.