The answer is found in Revelation 1:
4 John to the seven churches which are in Asia: Grace be unto you, and peace, from him which is, and which was, and which is to come; and from the seven Spirits which are before his throne; 5 and from Jesus Christ, who is the faithful witness, and the first begotten of the dead, and the prince of the kings of the earth. Unto him that loved us, and washed us from our sins in his own blood, 6 and hath made us kings and priests unto God and his Father; to him be glory and dominion for ever and ever. Amen. -Revelation 1:4-6 (KJV)
And in Revelation 5:
9 And they sung a new song, saying, Thou art worthy to take the book, and to open the seals thereof: for thou wast slain, and hast redeemed us to God by thy blood out of every kindred, and tongue, and people, and nation; 10 and hast made us unto our God kings and priests: and we shall reign on the earth. -Revelation 5:9-10 (KJV)
The kings that bring their glory and honor to the Lamb are the redeemed, who were from every nation and people. They were washed from their sins and made kings by Jesus and reign on the earth.
Everyone in the New Jerusalem does not stay perpetually within the city, for the very next verse makes a point to bring out the fact that the city gates are never shut, implying that the inhabitants come and go as they please:
And the gates of it shall not be shut at all by day: for there shall be no night there. -Revelation 21:25 (KJV)
Some of the kings go out into the earth, but still make trips back to the New Jerusalem in order to bring their glory and honor to the Lamb.