The 1st century Jews required an annual payment from each Jewish male to support the temple and its services. Apparently, Jesus hadn't paid by April 15th or whatever was the expected deadline (17:24). After the tax-collectors harangued Peter for Jesus' payment, Peter approached Jesus to ask why Jesus hadn't paid. Note that the text says that as soon as Peter arrived, Jesus spoke first (v. 25--divine omniscience), "From whom do kings of the earth collect duty and taxes--from their own sons or from others?" Peter knows full well that princes don't have to pay taxes to their dads (v. 26). Jesus affirms this as such to be true for Himself. Jesus does not have to pay a tax to His Father's temple. Similarly, as the miracle to follow shows (v. 27), Peter does not either. Through faith in Jesus who died for our sins on the Cross, we become sons and daughters of the King. We are no longer subject to the demands of the Law, because those demands have been met in Jesus Christ (Mt. 5:17). Jesus is the divine Son, but He laid down His rights as Son to bring us redemption (Phil. 2:5-11). At no point did He cease to be the divine Son--He could cause a fish to eat a silver coin and later bite the hook on Peter's fishing line to pay a simple tax. More importantly, our debts (what we owe because of sin and disobedience, Rom. 6:23) have been paid by this Son to make us Sons and Daughters of the King (John 1:12). We owe nothing because Jesus paid everything (Rom. 3:24-26; 2 Cor. 5:21).
NIV 1 Peter 1:18 For you know that it was not with perishable things such as silver or gold that you were redeemed from the empty way of life handed down to you from your forefathers, 19 but with the precious blood of Christ, a lamb without blemish or defect.
This doesn't mean that the IRS doesn't get their due on April 15th :) -- We are subject to human authorities (Rom. 13). But praise be to God we are no longer subject to Satan, the ruler of the air (Ephesians 2:1-10).