During its calibration and performance verification phase, the eROSITA instrument aboard the Spectrum-RG satellite performed a uniform wide-area X-ray survey of approximately 140 deg2, known as the eROSITA Final Equatorial Depth Survey (eFEDS). The primary aim of eFEDS is to demonstrate the scientific performance to be expected at the end of the eight--pass eROSITA all--sky survey. This survey will provide the first focussed image of the whole sky in the hard X-ray ($>2$ keV) bandpass. The expected source population in this energy range is thus of great interest, particularly for AGN studies. We used a 2.3--5 keV selection to construct a sample of 246 point-like hard X-ray sources for further study and characterisation. These sources are classified as either extragalactic ($ 90$ <!PCT!>) or Galactic ($ 10$ <!PCT!>), with the former consisting overwhelmingly of AGN and the latter active stars. We concentrated our further analysis on the extragalactic AGN sample, describing their X-ray and multi-wavelength properties and comparing them to the eFEDS main AGN sample selected in the softer 0.2--2.3 keV band. The eROSITA hard band selects a subsample of sources that is a factor of more than ten brighter than the eFEDS main sample. The AGN within the hard population reach up to $z=3.2$ but on the whole, they are relatively nearby, with median $z$=0.34 compared to $z$=0.94 for the main sample. The hard survey probes typical luminosities in the range $ X = 43-46$. The X-ray spectral analysis shows significant intrinsic absorption (with $ H >21$) in $ 20$ <!PCT!> of the sources, with a hard X-ray power law continuum with mean $< which is typical of AGN, but slightly harder than the soft-selected eROSITA sample. Around $10$ <!PCT!> of the hard sample show a significant `soft excess' component. The sampled black hole mass distribution in the eFEDS broad-line AGN population is consistent with that of the deeper COSMOS survey that probes a higher redshift population. On the other hand, the Eddington ratios appear systematically lower, which is consistent with the idea that the decline in SMBH activity since $z 1$ is due to a reduction in the typical accretion rate, rather than a shift towards activity in lower-mass black holes. The eFEDS hard sample provides a preview of what can be expected from the eRASS final survey in terms of data quality. This pilot survey indicates the power of eROSITA to shed new light on the demographics and evolution of AGN, and the potential for discovery of new and rare populations.