The most common English translation for the Hebrew word malach מלאך is "angel." Is that a good translation?
Well, it depends. If you think the definition of angel is (only) a divine, celestial being, perhaps with wings and a robe, then no. But as we'll see, that's not really what a malakh or an angel originally meant.
In Biblical Hebrew, malakh simply means "messenger." It can either refer to a divine messenger (in 124 cases) or a human messenger (88 times). To indicate that the malakh is sent by God, the word is conjugated with a name of God. If we look at Bereshit 32:2-4, we see examples of both kinds of messengers:
וְיַעֲקֹב הָלַךְ לְדַרְכּוֹ וַיִּפְגְּעוּ־בוֹ מַלְאֲכֵי אֱלֹהִים׃
וַיֹּאמֶר יַעֲקֹב כַּאֲשֶׁר רָאָם מַחֲנֵה אֱלֹהִים זֶה וַיִּקְרָא שֵׁם־הַמָּקוֹם הַהוּא מַחֲנָיִם׃
וַיִּשְׁלַח יַעֲקֹב מַלְאָכִים לְפָנָיו אֶל־עֵשָׂו אָחִיו אַרְצָה שֵׂעִיר שְׂדֵה אֱדוֹם׃
Jacob went on his way, and angels of God [malakhei Elohim] encountered him. When he saw them, Jacob said, “This is God’s camp.” So he named that place Mahanaim. Jacob sent messengers [malakhim] ahead to his brother Esau in the land of Seir, the country of Edom.
While it is possible that Jacob sent the same angels to his brother that he encountered earlier (as Rashi writes), the plain sense of the verse is that these were human messengers (as Ibn Ezra and Radak comment.) And there are many verses, such as Melachim I 19:2, where there is no question the malakhim are human.
Malakh derives from the root לאך, which has cognates in other Semitic languages, and means "to send." (It is not used as a verb in Hebrew, but it is used as one in Ugaritic and Arabic.) Some, like Stahl, say that לאך is related to the root הלך - "to go, to walk." The root לאך is also the origin of the word melacha מלאכה - "work, labor, craft." There are different opinions as to the connection between melacha and sending a messenger. Klein writes that melacha comes from the root meaning "to send", and therefore literally means "mission" (presumably of the person assigned to do the work.)
Others point to the phrase mishlach yad משלח יד, which literally means "sending of the hand", also means "work" (see for example Devarim 15:10,23:21). So perhaps if in that expression the laborers "send their hands" to do the work, in the parallel melacha (with the roots שלח and לאך being synonyms) maybe the hands are being sent as well.
In post-biblical Hebrew, the use of malakh began to change. It came to only mean the divine messengers, where as shaliach שליח was the term used for earthly ones.
When the Bible was translated into Greek, a word was needed to render malakh into Greek. The word chosen was angelos, Angelos was used to refer to both human and divine messengers, as Greek didn't have a word specifically for messengers sent by God. Later the Bible was translated into Latin as well. Latin, like Greek, didn't have a word specifically for divine messengers. So those translators used the already existing Latin nuntius for human messengers (related to "nuncio" meaning envoy), and borrowed the Greek angelos for divine ones. The word angelos entered the European languages with this meaning as well. So this is how angel, in English, came to mean specifically a divine, celestial agent.
But where does the Greek word angelos originally come from? There are a number of theories, but Klein's is particularly interesting. He says it has Semitic roots, and is cognate with familiar Hebrew words. He writes in his CEDEL:
...of Persian, ultimately of Semitic origin. Compare Akkadian agarru, 'hireling, hired laborer,' from agaru, 'to hire', which is related to Aramaic agar, eggar, 'he hired', (whence Arabic ajara, of same meaning), Hebrew iggereth, Aramaic iggera, iggarta, 'letter', properly 'message.' ... The sense development of Greek angelos [...] from a Semitic noun meaning 'hireling,' may be illustrated by the phrases 'hireling, hired messenger, messenger.'
We've actually discussed agar אגר as "to hire" before. But I didn't know then that igeret אגרת - "letter" was related to agar, and I certainly didn't know it could be related to "angel." Klein doesn't discuss the Persian bridge word between Greek and the Semitic languages, but Ben Yehuda does. He says that perhaps igeret comes from the Persian angar - meaning "story, narrative." The "n" in angar could explain the "n" in "angel" as well. From there it gets a little confusing. Perhaps the Persian was borrowed from Semitic, or maybe igeret came straight from the Semitic agar.
In any case, igeret certainly has Persian associations, as it appears only in the books of Esther and Nechemiah (which take place in the Persian period) and in Divrei HaYamim (whose composition is also from that time.) And just like in English a messenger is one who sends a message, so too in the Semitic-Persian-Greek development of the word, it's not hard to see how igeret and angelos are connected.
So to return to the original question - is "angel" a good translation for malakh? Well, considering both the fact that it was used specifically to translate malakh, and may even have roots in Semitic languages like Hebrew - I'd venture to say it's the perfect word for it!