well-pleasing: giving genuine pleasure to the one it is offered to, so that a gift, a life, or a person is gladly received rather than merely tolerated
This word describes whatever gives real pleasure to the one receiving it. It is built from the ordinary Greek word for pleasing (ἀρεστός) with a prefix meaning "well," so the sense is well-pleasing, not barely passable. In seven of its nine New Testament appearances the sentence names God or the Lord as the one being pleased.
Most of its uses reach back to the language of the altar. In the Old Testament an offering had to find acceptance before God would receive it (רָצוֹן), and Paul takes that vocabulary over: believers are to present their bodies as a living sacrifice, holy and pleasing to God (Romans 12:1), and the money the Philippians sent him is a fragrant offering, a sacrifice welcomed (δεκτός) and pleasing to God (Philippians 4:18). The point is not that God grudgingly allows such gifts. He takes pleasure in them.
From there the word widens out. It describes conduct and God's own will as something to be tested and found out (Ephesians 5:10; Romans 12:2), the obedience of children in a household (Colossians 3:20), and what God himself produces in his people (Hebrews 13:21). It can also describe a whole person rather than an act: the one who serves Christ in this way is pleasing to God (Romans 14:18), and Paul's settled ambition, whether at home in the body or away from it, is to be pleasing to him (2 Corinthians 5:9).
One use steps outside that Godward pattern. In Titus 2:9 household slaves are told to give satisfaction to their own masters in everything. The pleasure in view there is a human employer's, and the word carries the plain, workaday sense it has in Greek documents and honorary inscriptions that commend someone for serving well.