The simplistic description is this:
1. An electric current produces a magnetic field.
2. An oscillating (alternating) electric current produces an oscillating magnetic field.
3. An oscillating magnetic field "produces" an oscillating electric field, which in turn "produces" more oscillating magnetic fields, which in turn "produce" more oscillating electric fields, etc. via the time-derivative terms in Maxwell's equations. These oscillations propagate at speed c.
A more accurate version of step 3 is that oscillating magnetic fields are inevitably associated with oscillating electric fields, both propagating at speed c, again via the time-derivative terms in Maxwell's equations. This avoids the implication of a circular cause and effect chain.