In the last few chapters Calvin has expressed a lack of certainty regarding some aspects of the Trinity (i.e. usefulness of analogies), of Creation (i.e. why God waited an eternity before creating), and of angels (when specifically they were created). He chastises those who are overly curious about such details and refuses to speculate where Scripture doesn't give us any insight.
His humility is genuine. He doesn't fail to speak where Scripture does. He doesn't call everything we know into question (not a Bell-like false humility that questions if we can know what God has made plain through revelation). He simply refuses to speak about things that are too lofty, too mysterious, or on things that God hasn't chosen to speak. Here is a great quote from Book 1, Chapter 14 (about angels):
Not to dwell on this, let us here remember that on the whole subject of religion one rule of modesty and soberness is to be observed, and it is this, in obscure matters not to speak or think, or even long to know, more than the Word of God has delivered. A second rule is, that in reading the Scriptures we should constantly direct our inquiries and meditations to those things which tend to edification, not indulge in curiosity, or in studying things of no use. And since the Lord has been pleased to instruct us, not in frivolous questions, but in solid piety, in the fear of his name, in true faith, and the duties of holiness, let us rest satisfied with such knowledge...The duty of a Theologian, however, is not to tickle the ear, but confirm the conscience, by teaching what is true, certain, and useful...Bidding adieu, therefore, to that nugatory [of little of no consequence] wisdom, let us endeavour to ascertain from the simple doctrine of Scripture what it is the Lord's pleasure that we should know concerning angels.