Hebrews 13:7-9 meaning

The Hebrews believers ought to remember those who led them and taught them the word of God. Remember those who led you, who spoke the word of God to you; and considering the result of their conduct, imitate their faith (v 7). The Pauline Author encourages his readers to consider the results of their conduct or the result of them finishing ("teleo") what God set out for them to do. 

Throughout this letter, the Pauline Author has been admonishing his readers to endure until the end, to continue following God and walking in His path. It is encouraging to look at the lives of previous believers and see that their faithful walk with God was the right choice. We should consider those who walked faithfully with God before us, bother the result of their conduct and how to imitate their faith.

Even though Christian leaders may come and go and leave this earth, we can have comfort in knowing that Jesus Christ is the same yesterday and today and forever (v 8). We can also know that enduring until the end is worth it since Christ has assured us of this. And He is faithful.

Although these Hebrews did have some strong and faithful leaders, they also no doubt have heard strange teachings that do not align with what they were first taught. The Pauline Author wants them to stick with what they were taught at the beginning and not be led astray. Do not be carried away by varied and strange teachings (v 9).

The Pauline Author also writes that it is good for the heart to be strengthened by grace, not by foods, through which those who were so occupied were not benefited (v 9). The heart is strengthened by receiving God's grace through the ministry of Jesus Christ. The sacrificial system and religious practice (referenced here by the word foods) do not profit those who are focused on them. 

The Pauline Author's entire focus in this letter is on the inability of religious observance or regulations to cleanse our consciences of guilt for proper service to God. The better ministry of our better high priest, Jesus, is the only thing that allows us to draw near to God.