The resonance lines of helium in the Sun are several times stronger than expected, relative to lines of other ions. To explore the origins of this ''helium enhancement,'' we have studied data from the SUMER, CDS, MDI, and EIT instruments on the Solar and Heliospheric Observatory (SOHO). Time series data obtained in a quiet region and a coronal hole indicate that the spatio-temporal properties of the He i 584 8, and He ii 304 and 1084 8 lines are qualitatively unlike other chromospheric and transition region lines. Helium line intensities vary slowly compared to chromospheric oscillations and to transient transition region brightenings seen in other lines, yet they vary rapidly (both spatially and temporally) compared to the coronal radiation. This suggests that photoionization/recombination plays a minor excitation role in these lines. The Doppler shift of the 584 8 line shows a remarkably clear 4-8 mHz oscillation, with no accompanying line intensity oscillation. Transient brightenings are used to show that nonradial photon scattering might explain the previously found diffuse appearance of the network but cannot account for the reduced network/internetwork intensity contrast in the 584 8 line. We propose a new enhancement mechanism, based on arguments in a companion paper, in which predominantly neutral species such as helium diffuse across magnetic field lines into regions of hot coronal plasma, but charged ions do not. The enhanced internetwork helium emission may arise from the diffusion of helium atoms across the chromospheric canopy; the enhanced network emission may have contributions from diffusion from spicules. This mechanism may naturally explain why the 584 8 line shows Doppler shift, but not intensity, oscillations. Finally, if a mechanism such as ''velocity redistribution'' dominates helium emission, spectroheliograms of helium lines will be bright in regions of large temperature gradients parallel to the magnetic field. Differences between helium and other spectroheliograms may then reveal the relative contributions of ''classical'' and ''cool loop'' models to the observed emission.