The passage exemplifies the Stoic conception of death. While Stoicism was a diverse philosophical school, there are some principal unifying themes and views handed down from generation to generation. Crucially, Stoicism advises also a philosophical stance and path towards human's life and world. Hence, what Marcus Aurelius says ought to be understood from a philosophical perspective as expressed in Stoic terminology.
Since Stoic writings offer guidance for various parts of a socially and individually harmonious and meaningful life, they have broader readership than many other schools of thought have. In many cases, the original writings are translated interpretatively in consideration of such guidance. The original passage is as follows (bold added to the original and the corresponding words in the translation):
Πῶς πάντα ταχέως ἐναφανίζεται, τῷ μὲν κόσμῳ αὐτὰ τὰ σώματα, τῷ δὲ
αἰῶνι αἱ μνῆμαι αὐτῶν. οἶά ἐστι τὰ αἰσθητὰ πάντα καὶ μάλιστα τὰ ἡδονῇ
δελεάζοντα ἢ τῷ πόνῳ φοβοῦντα ἢ τῷ τύφῳ διαβεβοημένα: πῶς εὐτελῆ καὶ
εὐκαταφρόνητα καὶ ῥυπαρὰ καὶ εὔφθαρτα καὶ νεκρά, νοερᾶς δυνάμεως
ἐφιστάναι. τί εἰσιν οὗτοι, ὧν ��ἱ ὑπολήψεις καὶ αἱ φωναὶ τὴν εὐδοξίαν
παρέχουσι. τί ἐστι τὸ ἀποθανεῖν, καὶ ὅτι, ἐάν τις αὐτὸ μόνον ἴδῃ καὶ
τῷ μερισμῷ τῆς ἐννοίας διαλύσῃ τὰ ἐμφανταζόμενα αὐτῷ, οὐκέτι ἄλλο τι
ὑπολήψεται αὐτὸ εἶναι ἢ φύσεως ἔργον: φύσεως δὲ ἔργον εἴ τις φοβεῖται,
παιδίον ἐστί: τοῦτο μέντοι οὐ μόνον φύσεως ἔργον ἐστίν, ἀλλὰ καὶ
συμφέρον αὐτῇ. πῶς ἅπτεται θεοῦ ἄνθρωπος καὶ κατὰ τί ἑαυτοῦ μέρος καὶ
ὅταν πῶς ἔχῃ διακέηται τὸ τοῦ ἀνθρώπου τοῦτο μόριον.
An almost literal translation is given by Charles Haines as (published in Loeb Library):
How quickly all things vanish away, in the Universe their actual
bodies, and the remembrance of them in Eternity, and of what character
are all objects of sense, and particularly those that entice us with
pleasure or terrify us with pain or are acclaimed by vanity —how
worthless and despicable and unclean and ephemeral and dead!—this is
for our faculty of intelligence to apprehend; as also what they really
are whose conceptions and whose voices award renown; what it is to
die, and that if a man look at death in itself, and with the analysis
of reason strip it of its phantom terrors, no longer will he conceive
it to be aught but a function of Nature, but if a man be
frightened by a function of Nature, he is childish; and this is
not only Nature's function but her welfare; —and how man is in
touch with God and with what part of himself, and in what
disposition of this portion of the man.
It is important to note that theos (θεός: god), as a Stoic term, differs from familiar theological and metaphysical concepts found in other philosophical traditions or religions. For Stoics, physis (φύσις: nature) consists of a passive principle hyle (ὕλη: matter) and an active principle theos which is understood as a rational and benevolent entity that that brings order of the divine reason to the chaos of the material world. The Stoic God is not a separate entity from nature, on the contrary, it is the very essence underlying and maintaining the rational order of the cosmos. It is a governing and ordering force of the cosmos.
Thus, Stoicism rejects both the ancient anthropomorphic characteristics and a parallelism to the conception of God in the Abrahamic religions. In order to avoid confusion, some translators prefer such words as “deity” instead of “God,” or even, assimilate it to nature. Some others retain it, but with a lowercase “g.”
Notice that this conception of God is intimately tied to the idea of Logos (λόγος). The Stoic Logos is often described as an immanent and rational principle, providing coherence and structure to the cosmos. The connection between Logos and Theos reflects the Stoic understanding of a rational, ordered, and purposeful universe.
A Stoic ideal for us is to live in harmony with and to act in accordance with nature. We possess the ability to participate in the universal order and to become theoeides (θεοειδής: godlike). The seeds of this ideal in similar term is already manifest in Plato's thought. In the dialogue Theaetetus, Socrates says ([176a])
But it is impossible that evils should be done away with, Theodorus,
for there must always be something opposed to the good; and they
cannot have their place among the gods, but must inevitably hover
about mortal nature and this earth. Therefore we ought to try to
escape from earth to the dwelling of the gods as quickly as we can
[176b] and to escape is to become like God [ὁμοίωσις θεῷ], so far as
this is possible; and to become like God is to become righteous and
holy and wise.
Grasping the cosmic order and striving to achieve godlikeness foster acceptance of the natural cycle of life and death with equanimity. Death, a natural part of the cosmic order, is not to be feared but viewed and internalised as a certain aspect of existence.
Death is not an annihilation, but a transition, a return to the elements of nature from which man was originated. Thus, death is a reunion with this source; it is, as it were, a union as well as a communion with the Stoic God.
So far we have made some sense of the passage, however, the last sentence of the passage appears cryptic and detached from the others. First, we should keep in mind that these are the private notes Marcus Aurelius put down for his own use. So, that sentence should be regarded as an instruction to reflect on further for and by himself and a bridge to his next passage.
According to the Stoic tradition, death separates the soul from the body. Having considered the event of death through which the body withers away, evidently, Marcus Aurelius turns his attention to the soul. What he refers to as part and portion (μέρος and μόριον) must be not the bodily organs to get in touch with the Stoic God, but the constituents (or faculties) of the soul.
That brings us the Stoic views of mind and soul. The Stoics held a very interesting monistic perspective whose reconstruction and explication is highly controversial for their commentators. A convenient starting source is Scott Rubarth's IEP article Stoic Philosophy of Mind.
Whatever Marcus Aurelius' own response to his instruction might have been, it must be linked to the following passage in which he stresses that one need only attend the daimon (δαίμων: divine spirit) within oneself, and truly care for it.