Guinan is an El-Aurian, which according to Star Trek canon is a race of highly intelligent, Extremely long lived space-travellers who pre-date Earth's first contact with the Vulcan. This contact was just unbeknownst to mankind at the time, as they visited in secret.
All El-Aurians are said to have latent empathic abilities of a non-descript type, being widely known as a race of "listeners", but not seeming to have the direct mind or emotion reading skill of a Betazoid. Admittedly, that last part is conjecture, because we never see or "hear" a an El-Aurian use telepathy in the show proper... however, Guinan in particular has always seemed capable of telling a troubled crewmate just what they "needed to hear" in order to find the correct answer or at least "feel" better within a given situation.
Whether that is the result of some latent mental powers, or just her years of work as a bartender, one cannot be sure... but it's not impossible that is an expression of her species' latent ability.
Quote the Memory Alpha wiki:
El-Aurians prided themselves on being a race of listeners, and appeared to have a form of limited empathic ability. Some used this to help others, acting as advisers or confidants. A few turned their talent to more dubious pursuits, becoming con artists and tricksters, such as Martus Mazur, while Dr. Soran used his abilities to help bring his genocidal plan to re-enter the Nexus to fruition. (DS9: "Rivals"; Star Trek Generations) El-Aurians usually didn't experience difficulties with parents relating to their children, as El-Aurian children were usually good at listening to their parents.
El-Aurians have had encounters with numerous other alien species, including the Q and the Borg. They were the first race which disproved the Borg's logical fallacy of "resistance is futile"; even though their planet was taken over, the El-Aurians as a species escaped, survived and thrived. This longevity and the resultant encounters would likely mean they have found a few counter measures for dealing with other species as threats. Considering the power of the Q and the Borg, while outright "defeating" such opponents may not be a strong possibility, a long-lived practitioner like Guinan may well have refined and prepared plans for such tricky situations. Whether those would be of a technological, extra-normal or superhuman nature is up for debate.
Speaking of Guinan directly, she and "our" Q seemed to have some kind of ambiguous'personal history', hence him referring to her specifically as an "imp" and the fairly obvious animosity between the two. To my knowledge, this was never elaborated on in the show itself, and with the life-span of both, it could stem from one thing, or multiple dealings. As to how Guinan could have "countered" Q, it may have something to do with her natural empathic powers, or due to something specific to her as TruTrekkie postulated due to her time in the Nexus. If that were true, though, there should have been some type of "perception altering" for Picard as well, which we never see happen.
However, we have seen that there are Q weapons which could harm these beings, so its not impossible that Q knows Guinan has access to one such weapon; we've already seen that, for all her sweet temperament, empathy and understanding, Guinan is not above "packing heat" and pulling it out when necessary. So it's not improbable that she may have access to something which could be seen as harmful to Q's kind.....
Interestingly enough, Guinan is one of the beings on the ship whom Jean Luc Picard trusts implicitly with his life, and Q warned him "She is not what she seems." This could be indicative of three things:
- Q was trying to sow some dissention by throwing suspicion on Guinan, as a way of separating her from the Captain so he could have greater influence on Jean Luc.
- Guinan does possess a capacity for threat [mostly to him] simply by what she knows or could know, and doesn't want a consolidation of power with her and Picard.
- Plain, vindictive jealousy; Q has always shown a distinct interest in Picard, and this disliked El-Aurian having Picard's trust could have just been a thorn in his side, and that was a purely emotion-based jab.
While I don't think just "knowing the true nature of things" would be enough to "limit Q's power" as @DampeS8N said, I do think it could make his trickery more difficult if she possessed a limited ability to "see through" his alterations. And being so thwarted would be a minor annoyance to a god-being, one would think. However, if Guinana had any sort of power that could match or counter Q in a substantial way, it's reasonable to think she would have used such to aid the ship in other crisis situations, as opposed to sitting back and letting things unfold or resorting to a gun.
Then again, on the ship, she was dealing with mortals; Q was a different story. If that were the case, though, then the Q would have been no serious threat to the El Aruians, let alone them having to evacuate their planet to flee the Borg. It is possible that in all her years, Guinan specifically has learned some type of mental or extra-dimensional discipline [sort of like a "magic spell"] which could either prevent Q's power from directly influencing her, or even do some minor damage, but again, there is no solid evidence thereof.
Aside from the broadly expressed empathic ability and longevity, though, there is little to canonical support either Guinan herself, or her entire species having any other type of special abilities.