A solar flare is a sudden brightening of the Sun.
Other stars also flare (i.e., stellar flares).
Solar flares, which vary in brightness,
constitute a brief higher level of the Sun's (outward)
luminosity.
They are generally assumed to be the result
of magnetic reconnection in the Sun's magnetic field,
a plausible but complex process and current models
are limited in how much observed detail they match.
Exact modeling of the evolution of magnetic fields and their
reconnection is extremely challenging, and as far as I know, results
have been limited. The standard model of a flare is a qualitative
model, demonstrating how flares might occur, and for the last few
decades has been considered a workable explanation.