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You can use this skill to identify monsters and their special powers or vulnerabilities. In general, the DC of such a check equals 10 + the monster's CR. For common monsters, such as goblins, the DC of this check equals 5 + the monster's CR. For particularly rare monsters, such as the tarrasque, the DC of this check equals 15 + the monster's CR, or more. A successful check allows you to remember a bit of useful information about that monster. For every 5 points by which your check result exceeds the DC, you recall another piece of useful information
This is the only guidance we are given when using Knowledge to identify the abilities of Monsters. The question you ask is fairly common, and is one of those things in Pathfinder that will vary widely from GM to GM and group to group.
You'll likely get lots of suggestions here from other people how they do Knowledge checks, but I'll leave you with questions to determine how you want to use this ability.
1) Determine how OOC you wish to get. Most GMs I've encountered will not give out numbers, like AC, HP, saves, or SR. Instead they'll say, "The creature is resistant to fire", or, "You know bludgeoning weapons hit them with full effect", and that sort of thing.
2) Determine what a "bit of useful information" is. Is it a single entry in the statblock, such as SR, DR, or Immunity to Poison? Or is it the entire section on Special Attacks, Special Defenses, and Special Abilities. Doing an entire section may seem like a lot of information, but there are 3 sections, plus other possible areas of interest depending on the critter.
3) How does the player get this information? Does the GM determine what's "useful" and relay it to the player, or should it be more in the player's control? Letting the player ask a question, and the GM give an answer, puts determining what is "useful" in the player's hands. Whether you wish to run it that way is up to you.
I think because of the broad nature behind identifying monsters the Designers left this up to us to decide.
EDIT: 4) Come up with some guidelines to what you consider to be common, uncommon, and rare creatures. The entry says that goblins are common, and the tarrasque is rare, but other than that the entry is silent. In your campaign, maybe goblins were driven to near extinction and only one tribe is known to exist deep in the forest, thus making them a rare creature in your world. Some GMs limit extraplanar travel in their campaigns, so outsiders are considered rare, but if your world is constantly under attack by demons, maybe they're common. Or, if you're in doubt, just set the DC to 10+CR for everything until you feel comfortable determining what is common and rare.