This is the 1968th most frequent Japanese word.
だい
"だい" can mean "title," "topic," "cost," or "stand/base" depending on context.
Here, だい serves as an emphatic sentence-ender, used informally to convey surprise or emphasis.
この部屋はすごく広いんだい。
This room is very spacious!
だい is the stem of a word in this context (大事, 'daiji'), which means 'important'.
彼にとってそれは大事なことだい。
To him, that is an important matter.
In this example, だい is used colloquially as an ending particle expressing determination or enthusiasm.