Literal use for things that can explode or are related to explosions, such as 爆発的噴火 (explosive eruption).
The volcano caused an explosive eruption.
explosive (figurative); sudden and dramatic
Describes rapid, dramatic increases in sales, popularity, growth, etc. Often used with 増加, 成長, ヒット, 人気.
Sales of the new product grew explosively.
The song gained explosive popularity.