My opponent casts Oblivion Ring while I have a Grizzly Bears and a Hill Giant on board, and a Counterspell in hand. I don't mind if my opponent removes the Hill Giant, but for whatever reason the Grizzly Bears are key to my plans, and I would spend the Counterspell to keep them.
I have to choose before I know my opponent's plans: if I don't counter the spell, my opponent can target either of my creatures with the ETB effect; and if I wish to counter it, I must do so before they declare a target.
Often, players shortcut these kinds of spells: "I'll Oblivion Ring your Hill Giant". If I say "sure, that resolves" then the shortcut is applied all at once, and they can't interrupt their own shortcut to say "actually I'll take the bears instead." This opponent hasn't proposed such a shortcut, but I have the idea to ask "Targeting what?" before allowing the spell to resolve. Of course, "The spell has no targets" or "The spell is still on the stack" are good answers to this question, making me commit to countering before they commit to a target. But if my opponent says "Targeting the Hill Giant" then they have proposed a shortcut, and I can say "sure, that all resolves, the giant is gone", keeping my Grizzly Bears safe without spending the Counterspell. Conversely if they say "Targeting the Grizzly Bears" they've also proposed a shortcut, which I can interrupt with Counterspell.
But I wonder whether my question itself would be construed as passing priority, allowing the spell to resolve. After all, the spell isn't targeted, so if I'm asking about targets I must be referring to the ability. Does my intent matter here? Like if I really intended to get my opponent to leak information this way then throw the book at me, but if I thought of Oblivion Ring as a targeted spell and had no ill intent then I still have a window to counter the spell?