na-adjective, noun
plentiful; abundant; definitely extant
Emphatic expression meaning there is a lot of something, or that something definitely exists. Often used in casual conversation.
今年は雪が大ありだ。
There's a ton of snow this year.
彼の話には矛盾が大ありだ。
His story is full of contradictions.
たくさん is a neutral, standard word for 'many' or 'a lot'. 大あり is more emphatic and casual, often implying 'there is definitely a lot' or 'there is no shortage of'.
Compound of 大 (おお, 'big, great') + あり (the continuative form of ある, 'to exist'). Literally 'greatly exists'.