Hello,
I have never read The Prayer of Jabez, although it seems to me that most people who have read have one of two responses. When you ask somebody who loves the book what they think, the response is generally something like this:
And if you ask someone who wasn’t so fond of the book what they think about it, they generally, in my experience, react thusly:

But I was just looking at 1 Chronicles 4:9-10 and I was struck by a few things. To begin, Jabez isn’t mentioned anywhere else, he just appears, prays, and disappears again, right in the middle of a genealogy to which the chronicler makes no effort to connect him. Is he a son of Koz? A son of Harum? We don’t know; we aren’t told. I think that this is intentional, and it makes me think that the chronicler’s point was theological in nature. This fits with the overall theme of 1-2 Chronicles, which was written after the Jew’s return from exile to remind them of God’s covenant faithfulness in the past and their place as God’s people in the present. This is why it is generally more positive than 1-2 Kings; same general time frame; different purpose in writing.
Now, it’s possible (I would say probable, but what do I know?) that the original readers of Chronicles knew the context surrounding this prayer; who Jabez was, how he fit into the chronology, what the rest of his life looked like, and so on. Nevertheless, it’s possible to learn something from Jabez without knowing that context.
Even without the backstory there is a rhetorical force to this prayer; it says that God answers those who pray to him in faith. God can take a name given as a curse (Jabez, yah-vets, sounds like pain, o-tsev) and make sure that the curse does not come to pass. He can turn Jabez’ name around. A Jew reading this after the exile might remember that in Hosea’s prophecy Israel was given a name: No-mercy. The promise there was that someday God would take No-mercy and show her mercy, but after the exile that promise may have been obscured. The chronicler was reminding his readers that the same God who answered prayer then would be faithful to his people and his promise now.
It’s a two-verse word of encouragement from the chronicler.
-Daniel