Aims. We look to provide a detailed description of the SPectroscopic IDentification of ERosita Sources (SPIDERS) survey, an SDSS-IV programme aimed at obtaining spectroscopic classification and redshift measurements for complete samples of sufficiently bright X-ray sources. Methods. We describe the SPIDERS X-ray Point Source Spectroscopic Catalogue, considering its store of 11 092 observed spectra drawn from a parent sample of 14 759 ROSAT and XMM sources over an area of 5129 deg² covered in SDSS-IV by the eBOSS survey. Results. This programme represents the largest systematic spectroscopic observation of an X-ray selected sample. A total of 10 970 (98.9%) of the observed objects are classified and 10 849 (97.8%) have secure redshifts. The majority of the spectra (10 070 objects) are active galactic nuclei (AGN), 522 are cluster galaxies, and 294 are stars. Conclusions. The observed AGN redshift distribution is in good agreement with simulations based on empirical models for AGN activation and duty cycle. Forming composite spectra of type 1 AGN as a function of the mass and accretion rate of their black holes reveals systematic differences in the H-beta emission line profiles. This study paves the way for systematic spectroscopic observations of sources that are potentially to be discovered in the upcoming eROSITA survey over a large section of the sky.