NGC 604 is the most luminous H II region in M33. As the second nearest giant H II region, it can be observed in great detail over its entire extent. We have obtained high-resolution interference filter CCD images at six wavelengths to study the distributions of the ionized gas and massive stars, and long-slit echelle observations and TAURUS Fabry-Perot observations to study its detailed kinematic properties. We intend to use NGC 604 as a lab to investigate the physical mechanisms that are responsible for the large widths observed in the integrated velocity profiles of extragalactic giant H II regions. The morphology of NGC 604 is complex, showing numerous filaments and shell structures. We find that most of these shell structures are true expanding shells, and some have expansion velocities larger than 100 km s-1. Five large shells are identified and analyzed. We have modeled four of these shells as wind-blown bubbles, and found that the required stellar wind strength is higher than that implied by the stellar content. Supernova remnants (SNRs) must have contributed to the formation of some shells. The existence of SNRs is also supported by the bright diffuse x-ray emission in NGC 604. The known SNR M33 - 16 is recovered in the [S II]/Hα ratio map as well as the echelle spectra. The integrated velocity profile of NGC 604 consists of a core with a FWHM of 42 km s-1 and extended wings. The wings arise from fast expanding shells. To explain the integrated velocity profile width of NGC 604, we have constructed FWHM versus intensity diagnostic diagrams using individual profiles. These diagrams show that most points are contained in a narrow band with a median FWHM of 36 km s-1, suggesting the existence of velocity broadening mechanisms that are independent of position and surface brightness. The thermal broadening provides only a FWHM of ∼20 km s-1. The extra broadening of 30 km s-1 is within the range of virial motion expected from the total mass of NGC 604. The broadening from the 36 km s-1 to the integrated FWHM of 42 km s-1 is provided by the underlying broad line profiles that are associated with expanding shells powered by stellar winds and SNRs. Therefore, we conclude that the width of the integrated velocity profile consists of contributions from (1) thermal broadening, (2) stellar winds and SNRs, and (3) virial motion. The current observations of NGC 604 indicate that the contributions of the three mechanisms are roughly of similar orders of magnitude.