The word used in the above passage is normally translated as "work" - ἔργον.
This passage does not imply that Paul was professing monergism, as he preferences this particular remark with a commendation of the Philippians for their own action, namely their fellowship in furtherance of the Gospel (v. 5).
The concept of monergism was first seriously introduced by Augustine in the process of his combatting the Pelagian heresy. In some of his writings, which he later renounced, Augustine takes a position that man's free will plays no role whatsoever in his salvation. At one point he even went so far as to say that Peter essentially followed Christ involuntarily:
Will you dare to say that even when Christ prayed that Peter's faith
might not fail, it would still have failed if Peter had willed it to
Treatise on Rebuke and Grace, Ch. XVII
Augustine's views seemed to have taken hold in the west, but they were never taken seriously in the other four ancient Sees, which held to a doctrine of "synergy" of man's will with God's, rather than what has come to be called monergism. John Chrysostom, for example, comments on this passage:
Being confident of this very thing, that He which began a good work in you will perfect it until the day of Jesus Christ.
See how he also teaches them to be unassuming. For since he had
witnessed a great thing of them, that they may not feel as men are apt
to do, he presently teaches them to refer both the past and the future
to Christ. How? By saying, not, “Being confident that as ye began ye
will also finish,” but what? “He which began a good work in you will
perfect it.” He did not rob them of the achievement, for he said, I
rejoice for your fellowship, clearly as if making it their act; nor
did he call their good deeds solely their own, but primarily of God.
Homilies on the Epistle of St. Paul to the Philippians, Homily I
In brief, I believe that the "work" or "action" that Paul is referring to is, in fact, the work of God - the action of Grace. I do not believe, however, as stated above, that this is some sort of proof text for monergism.