This passage comes immediately after a passage in which our author rebukes the Hebrews for still being stuck on basic principles "when... ye ought to be teachers", and the famous contrast of those who feed on milk and meat. The first five chapters (as we now read the text) have been occupied with glorifying God and his salvation offered through the work of Christ, as well as hammering home the necessity of salvation beyond Moses, and Christ's fulfillment of the prophecies.
From here, the writer goes on to contrast in great detail the Mosaic covenant and Christ's new covenant, building to the crescendo of his message, which is that we now walk by faith, but have received the promise in Christ's death and resurrection, and we are therefore more certain of its fulfillment.
I see these verses as a transition: instead of the "negative" of the first section – all was not fulfilled in Moses, so look to Christ – the latter portion of the book of Hebrews has a positive message, that God has worked the same way, calling for faith, in all His dealings with us; and that we now are recipients of the final manifestation of His grace.
More immediately, however, I am intrigued by the short enumeration of "the principles of the doctrine of Christ".
[The Greek here (sourced from Perseus) reads τὸν τῆς ἀρχῆς τοῦ χριστοῦ λόγον, rendered in the Vulgate as inchoationis Christi sermonem, "the teaching of the beginning/foundational/first-laid things of Christ" (inchoationis appears to be a late Latin irregularity from incoho, "to begin"). The Greek original naturally has the same meaning, although ἀρχή in other contexts can be rendered rule or power as well – and while I hesitate to quarrel with generations of scholars, in some ways the translation "the doctrine of the dominion of Christ" – either referring to Christ's rule, or conceiving the Church as "the dominion of Christ" – might seem to fit nicely with the message of the author of Hebrews, although he does focus most on the priestly work of Christ, rather than his kingship.]
These are immediately referenced again as "the foundation", detailed in six items broken into three groups.
First, "repentance from dead works" and "faith toward God". In the context, the "dead works" refers clearly to what is elsewhere called "the righteousness of the law" – that is, men's own efforts to save themselves. This message of repentance and belief is clear and acknowledged at the heart of the Christian truth.
Last, "resurrection of the dead" and "eternal judgment". Again, these two doctrines are part of the eternal Christian message; as in the Creed, "...He will come again in glory to judge both the living and the dead... [I believe] in the resurrection of the dead".
But in the middle we have, "the doctrine of baptisms, and of laying on of hands". That baptism is a Christian sacrament has always been taught and accepted, as well as that the doctrine of baptism is important, to the point it has before divided the Church.
Less clear is the inclusion of "laying on of hands" (Greek ἐπιθεσεώσ χειρῶν, Vulgate inpositionis manuum, there is no difficulty here in the translation). Immediately a number of possibilities come to mind: the initial reception of a new believer; ordination to the clergy; the special apostolic gift whereby (cf. Acts 8) certain gifts were transmitted by laying on hands; or finally the intercession for the sick as initially recorded in James. In light of the surrounding phrases, though, it seems most likely that it refers to reception into membership: we then have a parallel structure where each set has a beginning (repentance, baptism, resurrection) and a fulfillment (faith, church belonging, judgment), that also parallels the overall structure of the epistle. Calvin also promulgates this argument, interpreting the laying on of hands to refer to the reception of covenant children.
Other less august persons take issue. Coffman touches on the subject, and identifies the laying on of hands with the apostolic gifts, using this to inveigh against the traditions of the hierarchical churches. Many other recent commentators seem to agree with him. Stedman agrees with Calvin for the most part as to the "message" of the text, but is content to note the various possibilities and the Judaic heritage of the practice. Most convincingly contrary, Guzik mentions another possibility, that the six elements are in fact not elements of the Christian faith, but initial ideas that both Jews and Christians would agree on: this fits equally well with the overall structure of the letter, and would explain an oddity.
To the modern Christian, or at least to me, it is a little strange to find that the Lord's Supper is not given a prominent place in this list of fundamentals, given our own arguments and divisions on the subject. Guzik's hypothesis would explain the exclusion. On the other hand, it is not really necessary, because an alternate explanation is equally plausible: the Communion receives far less prominence in the New Testament than it does in our modern ecclesiastical debates. Beyond the Institution, is is treated in any detail really only once, in I Corinthians. The reason seems to me clear: since even in that passage little examination is given to the actual question of what precisely happens, I deduce that, even as Communion is practiced today in all Christian churches, so even more so there was little question on the subject. Further, the modern difficulties arise largely out of questions of linguistics and precise description: such questions seem to have mainly arisen, on all topics, after the Apostolic Age.
What I also find odd is the effort – starting, as far as I can tell, with Calvin – to take the second phrase I have been examining with the first, as an appositive. While clearly a grammatical possibility, it would seem, from my perspective, unlikely. Linguistically, the only possible indication that a triple parallelism is not intended is the use of "τε" in the second phrase instead of "καἰ". The doctrinal argument, following Calvin, seems stronger: that if the second is not appositive, then we have as necessary to the doctrine of Christ – that is, salvation – some thing beyond repentance and faith. At the same time, it has to be admitted that in fact baptism is not identical with faith, even if it is an act of faith; and the New Testament, even Hebrews immediately after this passage, is full of warnings against those, presumably baptized, who fall away from the faith. Or again, as we find in the Great Commission: "He that believeth and is baptized shall be saved; but he that believeth not shall be damned." (Mark. 16:16, KJV).
As well as the small parallel movements from beginnings to fulfillment, however, there is a full progression throughout the six items. We can find here a description of the Christian life: from repentance to faith, faith to baptism, baptism to life in the church, life to resurrection (through death), resurrection to judgment. It seems to me not too much of a stretch to add an unstated seventh item: the eternal rest of Heaven.