At the very beginning of Act V, we see Ariel and Prospero discussing the success of their plan. In fact, Ariel suggests that the plan and Prospero's magic have had far stronger effects than they first anticipated. Ariel states:
Your charm so strongly works 'em
That if you now beheld them, your affections
Would become tender.
In short, Ariel states that if Prospero took the time to look at the castaways he would feel sorry for them and take pity on them. Prospero considers this idea and then states that because of his "nobler reason" he believes "the rarer action is / In virtue than in vengeance."
And because they are sorry for their prior sins and he has accomplished his goals, Prospero then orders:
Go release them, Ariel:
My charms I'll break, their senses I'll restore,
And they shall be themselves.
I think that you are talking about what Prospero decides at the very beginning of Act V, Scene 1.
Prospero gives two main reasons for showing mercy to his former enemies. First, he says that it is nobler to show mercy. There is more virtue in that than in taking revenge.
Yet with my nobler reason ’gainst my fury(30)
Do I take part. The rarer action is
In virtue than in vengeance.
The next thing he says is that their attitudes are important too. He says that they feel bad for what they did so he should forgive them.
They being penitent,
The sole drift of my purpose doth extend
Not a frown further.
I think it's likely that Ariel's comments matter because Prospero even asks him what he thinks and doesn't just ignore what Ariel says when he answers the question.