1. **θεόπνευστος (theopneustos)**

According to BDAG, this word is unique to Paul and literally means, "God-breathed" or "God-inspired" to use a more modern term.  Whether Paul invented the word or found it somewhere else, we do not know but it appears that this is the only instance of the word in 1st century Koine Greek writings.

2. **Meaning**

To help understand this term and what it involves, observe the text from which it came in 2 Tim 3:16, 17:

> All Scripture is God-breathed and is useful for instruction, for
> conviction, for correction, and for training in righteousness, so that
> the man of God may be complete, fully equipped for every good work.

Note that this means that the proper use of divinely inspired Scripture brings a change in the student by the following effects:
 - Good for teaching (about Godliness)
 - brings conviction of sin (John 16:1-8)
 - correction of erring people, that is, the student him/herself
 - training in righteousness (right doing)
 - makes the student of Scripture "complete", or better, "fully prepared"
 - equips the student for good works

This is no mere training in the normal sense - it is a power that changes people under the guidance of the Holy Spirit - miraculously.  That is, not only was the text of the scripture inspired by the Holy Spirit, but the when it is studied, the Holy Spirit impresses the student and brings about changes in the life of the student.

Note the parallel text in 2 Peter 1:19-21 -

> We also have the word of the prophets as confirmed beyond doubt. And
> you will do well to pay attention to it, as to a lamp shining in a
> dark place, until the day dawns and the morning star rises in your
> hearts. Above all, you must understand that no prophecy of Scripture
> comes from one’s own interpretation. For no such prophecy was ever
> brought forth by the will of man, but men spoke from God as they were
> carried along by the Holy Spirit.

That is, the "God-inspired" text of the Scripture was accomplished using the guidance of the Holy Spirit on the minds of the men who wrote it.  We see this many times such as: 2 Sam 23:2, Neh 9:30, Eze 2:2, 11:5, 24, Micah 3:8, Zech 7:12, 2 Peter 1:19-21, Rom 1:2, 3:2, Heb 3:7, 5:12, 9:8, Mark 12:36, Acts 28:25, 1 Tim 4:1.

I will resist the temptation to comment on the debate about verbal inspiration, vs, thought inspiration, vs, partial (as distinct from plenary) inspiration.  That is another question.