Special qualities are special abilities (Ex, Su, Sp) that are not special attacks or special defenses of a creature
In pathfinder, special abilities are divided between Extraordinary, Supernatural and Spell-like, and on creature's stat blocks, they are futher divided for the sake of organization on a creature's statblock as:
Special Attacks: special abilities that enhance a creature's attack (regular attacks), such as poison, paralyzis, drain energy, constrict, etc.
Defensive Abilities: special abilities that enhance a creature's defense (normally AC and saves), such as energy resistances, spell resistance, damage reduction, creatyre's type immunities, etc.
Special Qualities: special abilities that usually do not qualify as attack or defense, or abilities that are unique to that creature.
Extraordinary abilities are often mundane (and not "special" enough), so those are hardly listed as any of those subcategories, but there are lots of examples of that, like special attacks such as pounce or constrict.
You will notice, however, that the terms special quality and special ability are used interchangeably, with no special meaning to difference one or the other. For instance, check the zombie template stats:
Special Qualities: A zombie loses most special qualities of the base creature. It retains any extraordinary special qualities that improve its melee or ranged attacks. A zombie gains the following special quality.
Staggered (Ex)
Zombies have poor reflexes and can only perform a single move action or standard action each round. A zombie can move up to its speed and attack in the same round as a charge action.
But on the creature's stat block, staggered (an extraorindary ability) is shown under Special Qualities.
According to James Jacobs (Paizo's Creative Director), when asked about it the meaning of the term, he replied with:
As a general rule, something goes in the special quality line if it's not something that a monster uses to defend itself or to attack. They're usually things that don't have significant impact on combat. Think of "Special Quality" as a place to list monster powers and abilities that don't quite fit well anywhere else in the stats.
However, as he said, those are "generally" not significant on combat, but don't take that literally, as there are multiples examples of creature's special qualities that do have impact on combat, like the previously mentioned zombie's staggered ability.
Why the skeleton owlbear has grab?
That is an error on the SRD. The published ownbear skeleton has no statblock, it was published back in 3.5 and the SRD authors converted to pathfinder. The original creature entry was simply:
The skeletons lurk in the bone pits—six human skeletons to the west and an owlbear skeleton to the east.
(...)
Owlbear Skeleton CR 2
hp 32 (MM 226)
Which means the GM would have to do the templating himself, so it's not surprising that someone maintained grab as a mistake on the statblock.
On the anniversary edition of the curse of crimson throne, you will see that the officially published owlbear skeleton does not have grab.
