It could be either 1) a "preposizione articolata" (formed by the preposition "da" plus the article for plural nouns "i") 2) the second person present indicative or the second person imperative of the verb "dare" (to give).

Grammatically 'dai' is: - a preposition (preposizione articolata: da + i). The meaning of 'dai' when used as a preposition varies according to the context/sentence. Example: Andiamo dai nonni. In this case 'dai' means 'to'. - the second person present indicative or the second person imperative of the verb dare (to give). Example: Dai un osso al cane. However, 'Dai' is also an idiom with many different uses and meanings. Here are some examples. -Dai! In this case it's an expression used to pressure someone to do something quickly, like the English 'C'mon!' - Ma dai! In this case it's used to express astonishment; the meaning is the same of 'Davvero? Dici davvero?', which translates as 'Seriously? Are you serious?' -Dai... It can also be used as encouragement: 'Dai, non fare così', similar to the English 'Don't beat yourself up' - Dai leggiamo! When used before a verb it translates as 'Let's...!', in this example 'Let's read!' Feel free to ask any further questions.