adverb
Emphatic adverb used to intensify verbs and adjectives. Common in both spoken and written Japanese. Often translates to 'very much', 'greatly', or 'to one's heart's content' depending on context.
昨日のパーティーは大いに盛り上がった。
Yesterday's party was a lot of fun.
この結
I am very satisfied with this result.
休暇中は大いに楽しんでください。
Please enjoy yourself to your heart's content during the vacation.