anagkaios

This is by far the common use of the word, covering seven of its eight New Testament appearances. It describes a thing or an action as required, whether the pressure comes from need, from obligation, or from the logic of a situation.

The word ranges over two related shades. Sometimes it marks a thing you simply cannot get along without, like the parts of a body that keep it alive (1 Corinthians 12:22) or the pressing needs a community must supply (Titus 3:14). Other times it marks that something has to be done, and here the pressure has many sources: God's own plan (Acts 13:46), a reasoned pastoral decision (2 Corinthians 9:5; Philippians 2:25), the weighing of what will most help others (Philippians 1:24), or a conclusion that follows by necessity from a premise (Hebrews 8:3).

The adjective is close in force to the common verb δεῖ ("it is necessary, one must"), which is the usual way the New Testament speaks of what God's plan requires. The difference is mainly one of form: this word is an adjective describing a thing or a course of action as needful, while the verb states outright that one must act.

Across all these verses the plain sense stays the same. What shifts is the kind of necessity in view, and that is a question of context and theology, not of the word itself.

In its earliest use the word carried the idea of a binding force, and Greek writers applied it to people who are bound to you by ties of family or close friendship. So the same adjective that means "necessary" for things came to mean "intimate" for people: those in your inner circle, whom you cannot do without.

The New Testament uses this sense once, in Acts 10:24, where Cornelius gathers "his relatives and his close friends" to hear Peter. The phrase names his intimates, not merely people he found useful. This everyday use of the word for one's nearest kin and friends is well attested in ordinary Greek letters, in Josephus, and in classical writers.

The underlying picture is the same in both meanings: something (or someone) so tightly bound to you that life would be missing a part without it.