Importance of this scene: Stephano and Trinculo make the plan to kill Prospero and take over the island.
I came out the moon, i do assure thee
I'll show thee every fertile inch of thy island, I will kiss thy foot, I prithee, be my god.
I shall laugh myself to death at this puppy headed monster
Trinculo and Stephano trick Caliban into thinking they are gods so that Caliban can serve them. Stephano and Trinculo do this because they are tired of being servants to the king of Naples and want to be kings of the new island.
The scene contributes to a side story of the play, giving another challenge for Prospero.
Connection to History: The style in this play relates to how far back it's set, every character in this play is dressed relating back to how it was common to dress in the past in the kingdom of Naples