The word 'burgeoning' is the present participle, present tense of the verb 'burgeon', meaning to begin to expand or grow rapidly; to flourish; to put forth young shoots. The present participle of the verb also functions as an adjective.
Example sentence:
By the late 1980s, the computer industry was burgeoning. (verb)
The burgeoning industry in China is creating difficult environmental problems. (adjective)