Abarim Publications' online Biblical Hebrew Dictionary
יד
The mostly feminine noun יד (yad) is the Bible's common word for hand, but its figurative applications go far beyond those in English. And we also don't precisely know where it comes from. BDB Theological Dictionary reports that many scholars believe that our noun derives from a root that starts with the letter ל (lamed) and ends with a י (yod; BDB abbreviates this root to י־ל (l . . . y) but it's not clear what goes in the middle; לידי (l.y.d.y) would be an unusual long root).
But whatever the official etymology of the word יד (yad) might be, for all practical purposes (and to a Hebrew audience) our word looks like it has to do with the verb ידד (ydd) meaning to love or fondle, or the similar verb ידד (yadad), meaning to cast a lot. And both these actions obviously require the use of hands. The brilliant theologian Gesenius thought our noun might derive from the verb ידה (yada), which in the Bible means to praise, confess or give thanks, but which probably originated in the action of to throw or cast (which brings it quite close to the verbs ידד, yadad).
The usages of the noun יד (yad) fall into four categories:
One
Our noun יד (yad) predominantly denotes the human hand (Genesis 3:22, Judges 7:20, Ezekiel 39:3), and as such it became applied to anthropomorphized non-humans: God (Ezekiel 8:1-3) and cherubim (Ezekiel 10:8).
Two
Our noun's secondary meaning is that of strength or power. The idiom "in one's hands" meaning "in one's power" occurs all over the Bible (Joshua 9:25, Jeremiah 26:14). But our noun יד (yad) also serves directly as synonym for power. In 2 Kings 19:26 the prophet Isaiah speaks of the inhabitants of the fortified cities of Assyria and calls them קצרי־יד (qaseri-yad), literally small of hand = small in power; weak. Joshua 8:20 reads "There was not in them ידים (yadim; = hands) to flee", meaning: they lacked even the courage to flee, and Psalm 76:5 reads the colorful "none of the mighty men have found ידיהם (yadyhem; =their hands)", meaning they are without strength.
The notion of someone or something being in one's hands became extended to also include non-corporeal ideas: David speaks of injustice in his hands (Psalm 7:3) and Job denies there is violence in his hands (Job 16:17). Together with the verb מלא (male'), meaning to fill, our noun forms the colloquial phrase 'to the fullness of one's hand', which appears to denote a transfer or vestment of authority (Exodus 29:29, Leviticus 21:10).
Three
One application of our noun יד (yad) that doesn't correspond to any usage in English is probably derived from the observation that hands sit on the sides of a person's body. In Hebrew this became applied to inanimate items and came to denote the side of things, such as a road (1 Samuel 4:13), a gate (1 Samuel 4:18), a stream (Deuteronomy 2:37), land (Genesis 34:21) or a city (Nehemiah 7:4).
Four
Then there are a group of applications that are difficult to explain. Our noun is used to denote a monument (1 Samuel 15:12, Isaiah 56:5 — a display of might?) or a sign (Ezekiel 21:24 — a pointer?). It's used in the sense of a portion or share of grain (Genesis 47:24 — a handful?), but also of a share in the king (2 Samuel 19:43) or a helping of fighting men (2 Kings 11:7).
Our noun may denote a time; a repetition (Genesis 43:34 — from counting on one's fingers?), but also support structures (1 Kings 7:35, Exodus 26:17 — as placed on the side of the things they uphold?)