Abarim Publications' online Biblical Hebrew Dictionary
The verb לאך (la'ak) means to vicariously translocate one's mastery, will, purpose or intent. It may simply mean to charge a travelling courier with a message that relays one's instructions, but it may also describe forming a more static sign or monument that displays one's mastery, or indeed one's entire character and range of attributes.
This verb occurs across the Semitic language spectrum but curiously not in the Hebrew of the Bible. Its derived nouns, namely the masculine מלאך (mal'ak) and its feminine counterpart מלאכה (mela'ka), on the other hand, occur all over. These two nouns are separated only by gender, and in Hebrew, masculinity points toward individuality and singularity, whereas femininity points toward collectivity and multiplicity. Our nouns מלאך (mal'ak) and מלאכה (mela'ka) appear to be formed from the prefix מ (mem), which indicates agency, and literally mean "carrying agent of will".
Our feminine noun מלאכה (mela'ka) is commonly translated as "work" or "occupation" but really describes a more elaborate: "those deeds or items to which one applies one's will and mastery, and which are subsequently formed by one's will and thus display one's character and person". Hence this word is often translated as "craftsmanship" (Exodus 31:3), and it's also the word that describes the kind of "work" that wasn't allowed on the Sabbath: the kind that expressed the character of the artist or the mastery of a boss (Exodus 12:16, 20:9).
Rather striking, our word may also be used to describe cattle, or more specific: domesticated animals, or rather animals which behave according to the master's will (Genesis 33:14). The theme of the golden calf (Exodus 32:4) and the altar made from un-hewn stones (Exodus 20:25) clearly play with the idea that, although it's certainly beneficial to press one's will on one's surrounding, true stewardship of nature and true mastery over nature come not from violently subjecting nature but rather from first learning how nature works and then assuming and adopting a character that is the same as that of nature, and thus also as that of its Creator.
The earliest expression of our root occurs in Genesis 2:2, where it is stated that on the seventh day, Elohim completed his מלאכה (mela'ka). Most translations interpret this word blandly as "work" but it obviously goes far beyond this. God's creation reflects no less than the Creator's invisible attributes, his eternal power and divine nature, and until God's Word appeared in the Flesh, the careful observation of God's creation was the only way to know him (Romans 1:20).
The masculine version of our word, the noun מלאך (mal'ak), simply means messenger and is also the Hebrew word for angel. Or said otherwise, the Bible makes no distinction between a human messenger or an "angelic" one. This in turn demonstrates that the expectations of how congress with the divine should work differs strongly between us moderns and the ancients. Intuition may dictate that our primitive ancestors saw "angels" everywhere, but instead they didn't even have a word for "angel". In fact, it may very well be that our modern idea of blond and burly wing-flapping and sword-wielding dudes from heaven is idiotic beyond belief, and that the Biblical idea which the modern angel caricaturizes actually tells of an aspect of the human psyche that only the most sophisticated minds may recognize. For a much deeper look at angels and the psychology behind them, read our article on the Greek equivalent of our word, namely αγγελος (aggelos).
The plural of our noun מלאך (mal'ak) may describe divine messengers (Genesis 19:1, Job 4:18, Psalm 78:49) but mostly refers to human ones (Genesis 32:3, Numbers 20:14, Deuteronomy 2:26, Joshua 6:17, Judges 6:35, Isaiah 14:32). The singular form of our noun may refer to a human messenger (1 Samuel 23:27, 2 Samuel 11:19, 1 Kings 19:2), but mostly refers to divine ones:
The term מלאך יהוה (mal'ak yhwh), or "Messenger of YHWH" is introduced in Genesis 16:7, as he appears to Hagar, who was then pregnant with Ishmael. Just one chapter prior, the term דבר יהוה (dabar yhwh), or "Word of YHWH" was introduced in the story, as he had appeared to Abraham (15:1), which appears to suggest that where an encounter with the Word results mostly in a formal and intellectual understanding of the Law of Nature, an encounter with the Messenger mostly results in an intuitive grasp of the Way Things Are.
The second time that Hagar flees, this time with young Ishmael in tow, she has an encounter with מלאך אלהים or the "Messenger of Elohim" (21:17). Abraham is prevented from slaughtering Isaac by the Messenger of YHWH (22:11), and calls the place where that happens YHWH-jireh, or YHWH Provides (22:14). The Messenger of Elohim again shows up to address Jacob, and does so in a dream (31:11). Later Jacob recounts his adventures and speaks of המלאך (hamal'ak), or The Messenger (48:16).
The Messenger of YHWH appears to Moses in the bush (Exodus 3:2) but the Messenger of Elohim leads Israel in the form of the pillar of cloud and fire (14:19). On the mountain, Elohim promises Moses that he will send a Messenger to lead, to guard, to direct and even to wage war against natives, which may or may not suggest that this is a whole other Messenger (23:20, 33:2).
Only in Haggai 1:13 occurs a third noun, מלאכות (mal'akut), which appears to be a plural word used singular (like our word "people"). It means something like messagings.
Also note the similarity between our noun מלאך (mal'ak), meaning messenger, and מלך (melek), meaning king. These two words are not etymologically related, but their similarity seems to have helped to form the definition of a king in Israel.