to burn intensely
come under fire; be severely bashed/crucified
Nowadays, a myriad of people 炎上する after making inflammatory remarks or uploading videos of their stupid and inappropriate/illegal behaviour on social media. A lot of them do this on Twitter in particular, and hence some people call Twitter “馬鹿発見器” (“idiots detector”) or バカッター (バカ + ツイッター).
Some people make 炎上 on purpose to attract attention for their benefit. This type of 炎上 is called “炎上商法 (えんじょう しょうほう, enjou shouhou)”, where “商法 (しょうほう, shouhou)” means “commercial strategy”. For instance, some celebrities are often criticised for doing this by posting provocative/inflammatory oppinions on social media to increase their followers. Similarly, some companies advertise their products with controversial or sexual lines.
Note that this word is also used literally as in the second example sentence below.
That athlete made racist remarks and came under fire.
A car caught fire after a collision