to be full; to fill; to reach completeness
The basic movement of this word is fullness: something becoming full, something being actively filled, or a measure reaching its appointed limit. The same root drives all four senses, moving from simple spatial filling to the completion of time, the fulfillment of a divine word, and a technical ritual act.
The intransitive and transitive uses are the most common. The earth fills with violence (Genesis 6:11), God fills heaven and earth (Jeremiah 23:24), and at the dedication of the tabernacle the glory of the LORD fills the dwelling so that Moses cannot enter (Exodus 40:34-35). The active sense runs just as widely: God fills artisans with the Spirit of wisdom (Exodus 31:3), a mother fills a flask with water (Genesis 21:19), and armies fill quivers before battle (Jeremiah 51:11).
The temporal sense rests on the same image: days or years reaching their full count, the way a vessel reaches its brim. A woman's days are fulfilled before she gives birth (Genesis 25:24), an exile lasts until seventy years are completed (Jeremiah 29:10), and a vow is observed until the days of separation are full (Numbers 6:5). The fulfillment of a divine word extends this: a word spoken by the LORD reaches its appointed end just as time does (1 Kings 2:27, 2 Chronicles 36:21).
The idiom "fill the hand" is a technical term for installing a priest into office, and it occurs so consistently in the priestly legislation and related texts that it functions as an established expression for ordination (Exodus 28:41, Leviticus 8:33). The precise background of the phrase is debated, though most scholars connect it to the transfer of a token or portion that confirmed the installation.