... continued from Wednesday.
Hebrews helpfully tells us the main teaching point of the sermon: "The main point of what we are saying is this: We do have such a high priest, who sat down at the right hand of the throne of the Majesty in heaven, and who serves in the sanctuary, the true tabernacle set up by the Lord, not by a mere human being" (8:1-2). This is not just an idea the author of Hebrews is excited about. There were very real practical implications of this truth for the audience.
For one, I already mentioned the obscure comment Hebrews makes at the end, where the author tells this community not to be "carried away" by strange teachings (13:9). He then reinforces the fact that believers have a sacrificial altar from which we can eat that those who rely on normal Jewish means of atonement can't eat. Talk about an obscure statement, at least from our perspective 2000 years later. They no doubt knew what the author was alluding to but we unfortunately aren't there.
You probably know that the temple in Jerusalem, while it was standing, offered sacrifices every day not only for the Jewish people but for others like the emperor as well. Even if you were a Jew living in Greece or Rome, you knew that every day the priests in Jerusalem had your back with God. In fact, Jewish males were supposed to pay a "half shekel" tax (about a day's wage) to the temple every year to support it. 
Hebrews 13 doesn't sound like it is talking about the "business as usual" sacrifices, which the author considers to have been legitimate, even if ineffective, foreshadowings of Christ's death. So it doesn't seem likely that the author would refer to them as "strange teachings" (13:9). No, this comment sounds like some of the strange ideas you hear from people in the church today as they think a little too much about questions we just don't have the answers to.
So you can hear someone in the first century say, "How are we going to take care of atonement now that the temple is gone?" That is, if Hebrews was written after the temple was destroyed. Before the temple was destroyed, you could hear someone asking, "How can I get the benefit of the temple sacrifices if I live way out here in Rome or somewhere else?"
When there aren't clear answers to our questions or when there is a gap in what the Bible tells us, it is hard for people just to let the question go unanswered. This is the point where preachers can get a little strange from the pulpit or you have a strange idea in a small group or Sunday School class. Worse, this is the point where a strong personality might go start a new denomination or a cult. You ask, "Whatever happened to those ten lost tribes of Israel?" and before you know it, you have the Mormon church!
We don't know what the strange teaching was that Hebrews mentions, but it had to do with atonement and it apparently connected some "foods" (13:9), possibly some meal that was part of some synagogue. It was obviously Jewish in nature, since Hebrews connects it with "those who minister at the tabernacle," an allusion to the sanctuary that God instructed Moses to construct in the wilderness.  We can only guess at the details, but I can personally imagine that the time after the temple's destruction gave rise to lots of strange ideas about how to keep getting atonement now that the temple sacrifices were gone.
In response, the author of Hebrews repeats that believers have a much better altar, the altar of Christ's atonement. Did Hebrews have communion in mind? It is often suggested and is very tempting, although we cannot know for sure.  What we can know for sure is that Christ's atoning death has once and for all removed any necessity to seek our peace with God anywhere else other than in Jesus...
 Cf. Matt. 17:24-27. See ***, "Taxes," in Dictionary of Jesus and the Gospels, J. B. Green, S. McKnight, I. H. Marshall, eds. (Downers Grove, IL: InterVarsity, 1992) 806.
 Again, I personally think this theoretical reference to the tabernacle fits better a context after the temple was destroyed. Those who think the audience of Hebrews consisted of Jews tempted to return back to Judaism might suggest that this point of conflict arose as Jewish believers were kicked out of the synagogues and were tempted to return so that they could partake of such meals. See B. Lindars, The Theology of the Epistle to the Hebrews (Cambridge: Cambridge University, 1991).
 It is so hard for us to resist reading our current language and practices into the biblical text. This is the danger of anachronism, reading our definitions for words and our ways of thinking into the biblical words.