。
I'm happy to be invited to dinner.
Literal
Dinner [to-に] invite-[passive-された]-[so-て] happy.
招待される is the passive of 招待する — 'to be invited.' The te-form 招待されて chains to the i-adjective うれしい ('happy, glad') to express cause: 'happy because [I] was invited.' This te-form-for-cause pattern is the standard way to express emotional cause in Japanese.