In The Tempest, what is the significance of the masque in Act IV scene 1?
I think the significance of the masque that Prospero summons up with his magical powers lies in the way that he sends through it a very clear message to his future son-in-law about the kind of behaviour he expects from him with regards to his marriage to Miranda. Let us remember that Prospero only presents the masque after a frank discussion of sexuality where Ferdinand refers to Miranda's virginity in a rather vulgar fashion:
As I hope
For quiet days, fair issue and long life,
With such love as 'tis now, the murkiest den,
The most opportune place, the strong'st suggestion.
Our worser genius can, shall never melt
Mine honour into lust, to take away
The edge of that day's celebration
When I shall think: or Phoebus' steeds are founder'd,
Or Night kept chain'd below.
Here Ferdinand refers to his sense of excitement at the first night of love he will share with Miranda, which shows him to be a rather lustful individual who is rather too focused on sex and the claiming of Miranda's virginity for Prospero's liking.
As a result it is particularly relevant that the characters of Juno, Ceres take a very harsh stance of lust and love. Together, these two deities symbolise family and prosperity, giving the couple a blessing that moves away from any suggestion of sex or love. Consider the way that there is no reference to love, feelings or sexuality. Instead, the role of marriage in society is emphasised. For example, when Ceres asks Iris where Venus and Cupid are, the deities representing the powers of love and sex, Iris responds that she hopes they will not appear, because it was their influence that was responsible for the kidnapping of Persephone by Pluto, the god of the underworld. We are told that Venus and Cupid had wanted to spoil the purity of this union, but they had been kept away thanks to the other deities. If we consider the context of Ferdinand's remarks to his future father-in-law, perhaps we can see such remarks as a very strong hint as to the kind of role Propsero wants sex and love to have in his daughter's marriage.