I've looked through some of the manuals, and find the best explanation, supported by all the examples I can find of explicit or implicit use of Counterspelling for characters and spells, to be in the Spellcasting "Step-by-step How To" on pages 182-184 of
SR4A:
QUOTE
Spells cast on living or magic targets are often resisted, and an
Opposed Test is required. For area spells, the magician rolls only once,
and each target resists the spell separately. The target resists physical
spells with Body and mana spells with Willpower. If the target is also
protected by Counterspelling (p. 185), she may add Counterspelling
dice to this resistance test.
(emphasis mine)
This use on non-living targets is borne out explicitly, for example in the Shattershield spell description in
SM which attacks a magical barrier, and implicitly in other spells such as Decrease Reflexes, which can be used against critters as well as characters.
So it appears to me that Counterspelling can be used to protect any living or magic target that gets a resistance roll against attack by a spell. I don't think it can be used to protect things that do not get a resistance roll, but only an Object Resistance. Furthermore, I don't think it can be used to protect against other kinds of magical attack, such as a spirit power, Astral Combat, or a Counterspelling attempt to bring down a sustained spell.
Too bad about that last one. It would be kind of cool to see two magicians duelling, Couterspelling the other's Counterspell until one fails.