Context. The [C ii] 158 µm fine-structure line is one of the dominant coolants of the neutral interstellar medium. It is hence one of the brightest far-infrared emission lines and can be observed not only in star-forming regions throughout the Galaxy, but also in the diffuse interstellar medium and in distant galaxies. [C ii] line emission has been suggested to be a powerful tracer of star-formation. Aims. We aim to understand the origin of [C ii] emission and its relation to other tracers of interstellar gas and dust. This includes a study of the heating efficiency of interstellar gas as traced by the [C ii] line to test models of gas heating. Methods. We make use of a one-square-degree map of velocity-resolved [C ii] line emission towards the Orion Nebula complex, including M43 and NGC 1977. We employ Herschel far-infrared photometric images to determine dust properties. Moreover, we compare with Hα emission from the ionized gas, Spitzer mid-infrared photometry to trace hot dust and large polycyclic aromatic hydrocarbons (PAHs), and velocity-resolved IRAM 30m CO(2-1) observations of the molecular gas.Results. The [C ii] intensity is tightly correlated with PAH emission in the IRAC 8 µm band and far-infrared emission from warm dust. However, the [C ii] intensity depends less than linear on the 8 µm and far-infrared intensity, while 8 µm and far-infrared intensities are approximately linearly correlated. The correlation between [C ii] and CO(2-1) does not show a clear trend and is affected by the detailed geometry of the region. We find particularly low [C ii]-over-FIR intensity ratios towards large columns of (warm and cold) dust, which suggest the interpretation of the "[C ii] deficit" in terms of a "FIR excess". A slight decrease in the FIR line-over-continuum intensity ratio can be attributed to a decreased heating efficiency of the gas. Furthermore, we find that, at the mapped spatial scales, predictions of the star-formation rate from [C ii] emission, like most other tracers, underestimate the star-formation rate calculated from YSO counts in the Orion Nebula complex by an order of magnitude. Conclusions. [C ii] emission from the Orion Nebula complex arises dominantly in the cloud surfaces, many viewed in edge-on geometry. Most of the [C ii] emission stems from the extended fainter outskirts of the irradiated regions, while the [C ii] intensity is deficient with respect to the total far-infrared intensity in the brightest regions. [C ii] emission from extended faint cloud surfaces may contribute significantly to the total [C ii] emission on galactic scales.