According to verse 24, Paul is here talking about the glories of the new covenant relationship as compared to the old covenant idea of human effort alone. Sinai is used to represent the old covenant (verses 18-21), and Jerusalem is used to represent the new. In Galatians 4:24-26, the very same parallel is made symbolising the two covenants by Sinai and Jerusalem.
Some have interpreted these verses to mean that souls go immediately into the heavens at death to appear at the judgement bar. But please notice that these people come "to Jesus the mediator of the new covenant." Those who are saved in heaven will no longer need a mediator such as is described here. Sin will have ceased for them.
Paul is actually describing the life of a Christian here in this world as he begins to experience the joys of the new covenant relationship. Such a Christian comes to:
1. "Mount Sion ... the city of the living God." Peter speaks of the church in similar language: "lively stones a spiritual house." 1 Peter 2:4-6.
2. "An innumerable company of angels"---descriptive of the angel ministry for the saints mentioned in Hebrews 1:7.
3. "The general assembly and church of the firstborn, which are written in heaven"--another description of the body of Christ on this earth. Paul spoke of his fellow labourers as those "whose names are in the book of life." Philippians 4:3.
4. "God the Judge of all." This is parallel language to Hebrews 4:16, which says, "Come boldly unto the throne of grace," and to Hebrews 7:25, which says, "He is able also to save them...that come unto God by Him."
5.    "The spirits of just men made perfect"--not disembodied spirits as some imagine, but the kindred spirit of Christian with Christian. Paul contrasts those who walk "after the flesh" and those who walk "after the spirit." But these are real people who have spiritual natures that are sanctified through the blood of the new covenant. Compare Hebrews 10:14: "For by one offering he hath perfected for ever them that are sanctified."