Why did the writer of Hebrews included Hebrews 13:8? What's it for?

Hebrews 13:8 says: "Jesus Christ is the same yesterday, today, and forever." 

Yes, it is true that the Lord Jesus Christ is immutable in His nature, but the point of Hebrews 13:8 is to establish the readers in grace, in the person and priesthood of the Lord Jesus Christ. The best way to understand Hebrews 13:8 is to understand it in the overall point of the book of Hebrews. 

Heb 5:6 As He also says in another place: "You are a priest forever According to the order of Melchizedek";

 Heb 6:20 where the forerunner has entered for us, even Jesus, having become High Priest forever according to the order of Melchizedek.

 Heb 7:17 For He testifies: "You are a priest forever According to the order of Melchizedek."

 Heb 7:21 (for they have become priests without an oath, but He with an oath by Him who said to Him: "The LORD has sworn And will not relent, 'You are a priest forever According to the order of Melchizedek'"),

The Hebrews were tempted to go back to the law and the temple worship with all the priests under law. Apparently, they were tempted to think that Christ's priesthood was something like that of the priesthood under the law --- it passes from one person to another since they were prevented by death to live on and continue their ministry. 

They don't need other priests. Christ is the priest that lives on forever and ever to intercede for them. He is the same priest that they need yesterday, the same priest that they need today and the same priest they will be needing tomorrow and forever. 

Heb 7:25 Therefore He is also able to save to the uttermost those who come to God through Him, since He always lives to make intercession for them.