(covers information from several alternate timelines)
A solar flare (or solar plasma eruption) is an explosion in a star's atmosphere, that accelerates plasma into space at great speeds. By the 24th century, various techniques existed to trigger solar flares, including particle beams and electromagnetic pulses. The concentration of cosmic rays that can accompany a solar flare can be measured on the Ritter scale.
In 2255 of the alternate reality, military shuttles were sensitive to solar flames and one cropping up might cause the occupants to be boiled in their seats, at least if a panicking Leonard McCoy was to be believed. (Star Trek)
In 2266, a solar flare, accompanied by high levels of cosmic rays, was discharged by the sun in the Minarian star system. The USS Enterprise was forced to leave orbit around one of the Minarian planets to protect its systems from the solar flare. Meanwhile, a landing party from the Enterprise – consisting of Kirk, Spock, and McCoy – remained on the planet's surface, judging that the planet's atmosphere would shield them from the flare's effects. (TOS: "The Empath")
In 2364, Lieutenant, j.g. Geordi La Forge told Captain Jean-Luc Picard that the solar flare activity on a star the USS Enterprise-D was studying was increasing. The shields were weakened by the flare activity, but managed to hold. (TNG: "Symbiosis")
While investigating a Dyson sphere, the USS Enterprise-D was pulled inside the sphere and observed the unstable star within expelling a solar flare, which Data indicated as magnitude twelve, class B. (TNG: "Relics")
In 2371, Grand Nagus Zek talked to a representative of a planet which had been affected by solar flares, damaging its agriculture. The Ferengi leader agreed to provide the planet with Kohlanese barley. (DS9: "Prophet Motive")
In 2373, Lieutenant B'Elanna Torres listed a solar flare as one of many factors that could interfere with USS Voyager's attempt to bring the Barzan wormhole to them with verterons. (VOY: "False Profits")