Quite literally, it grew out of a fissure in a cornfield in February 1943, continuously erupting until 1952.
Parícutin Volcano image from the USGS in 1946. Image source: Oregon State University Volcano World.
What does the evidence suggest for precursor geological processes occurring immediately prior to the Parícutin Volcano eruption in 1943?
Erlund et al. (2010) extensively studied the basal tephra, their results suggest the following occurred immediately prior to the 1943 eruption:
This magma movement is likely to have caused the ~45 days of seismic activity that was noted before the fissure opened up in the cornfield, initiating the Parícutin volcano eruption.
There is a more modern day analogue to the associated seismicity, based on models developed by Gardine et al. (2011) from an earthquake swarm that occurred near to the Parícutin volcano in 2006, where the low magnitude earthquake swarms occurred in clusters that demonstrated reasonably rapid ascent and lateral movement - suggesting not only a possible mechanism for magma ascent, but also demonstrates the region is still very active.
References
Erlund et al. 2010, Compositional evolution of magma from Parícutin Volcano, Mexico: The tephra record, Journal of Volcanology and Geothermal Research
Gardine et al. 2011, Dike emplacement near Parícutin volcano, Mexico in 2006, Bulletin of Volcanology
Langridge et al. 2013, Preliminary paleoseismic results from the Pastores fault and its role in the seismic hazard of the Acambay graben, Trans-Mexican Volcanic Belt, Mexico, Revista mexicana de ciencias geológicas