(If you want to read a quick reply to this question, I recommend you read this article.)
This, in many different versions, is a very old question. It's a kind of paradox we face when dealing with the concept of an all-powerful being. Some attribute it to the Moslem thinker, Ibn Rushd (Averroes). More than anyone, it was Maimonides who answered it with his "negative theology"—which was later adopted by Thomas D'Aquinas and became standard Roman Catholic theology, as well.
Negative theology is much easier to understand if you are familiar with Aristotelian logic—which gave birth to the question to begin with. But I'll try to describe it here in short.
In Aristotelian thought, everything is a duality. This was the way of thinking about things up until the time of Rene Descartes and the early rationalists who began to discuss matter as a measurable quality. Until then, there was (1) the thing itself and (2) its qualities, or predicates.
For example: Water flows. The wind blows. Rocks are heavy, etc. But flowing is not water, blowing is not wind and heaviness is not rocks. So there is water, and there is this quality that it has to flow. But the water itself is not the flowingness of the water. Neither is the wind its blowingness. Or the rock its heaviness. And the same with everything else that exists: The qualities of a thing are not the thing itself—rather, the thing itself has qualities.
Maimonides realized that this could not apply to G‑d, since G‑d is a perfect oneness. A perfect oneness can't have any dualities. So to say that G‑d is kind, or G‑d is wise, or G‑d is strong—that's not going to work, since it implies dualities and multiplicities in G‑d.
But nevertheless, all these things—kindness, wisdom, strength and more—all come from G‑d, since He created all things. Like the psalmist rhetorically asks, "The one who implants the ear doesn't hear?" So if hearing exists in the creatures that He created, He must also have a quality of hearing. The same with wisdom and kindness—for us to have these qualities, they must first begin with G‑d.
So Maimonides answered that G‑d really has no attributes. When we attribute strength, kindness, wisdom, etc. to G‑d, what we mean is that He does not lack these qualities, since, after all, they also extend from Him—as does everything extend from Him. But He cannot be described by any of them.
In fact, Maimonides went so far as to say that G‑d cannot even be said to have existence. We cannot say that G‑d exists—since that would imply that there are two things, G‑d forbid, about G‑d: That He is G‑d and that He exists. Rather, G‑d cannot be predicated with any quality, even that of existence.
Although Maimonides himself notes that this is a matter that the human mind can never truly fathom, nevertheless Rabbi Schneur Zalman of Liadi ("The Alter Rebbe") provides two helpful metaphors: One from the relationship of the sun and its light, another from the relationship of speech to the human psyche.
Let's say you see a ray of light from the sun shining in through your window. So you ask this ray, "Where did you come from?" It answers, of course, that it came from the sun. So you ask it, "Let me see what you look like as you are in your source within the sun." So it takes you there (in your nuclear fusion resistant suit) and you look about and—hey, there's no ray here! But why? Doesn't the ray start here? Yet all there is here is one single source of light. The entity of the ray is entirely absorbed within that oneness.
Same thing (almost) with a word of speech. Where did that word you spoke come from? Well, it arose out of a feeling you had, or some perspective of things you had in your mind. But there, in that raw feeling or mental perspective, there are no words. Yet words arise from that place.
So too—but in an infinitely more perfect way—in G‑d's perfect oneness there is no wisdom, no understanding, no knowledge, no kindness, no strength, no nothing. Just a perfect oneness. Yet from that oneness, all things arise. Go figure. Or don't. As Maimonides implies and the R. Schneur Zalman spells out, the human mind only understands things as they are within it. We are composites of many different qualities, so we cannot conceive a perfect oneness—just as we cannot conceive of something that has only one side but no back, so we cannot conceive of that which neither is nor is not. Or that which is neither strong nor not strong, yet from which all strengths extend.
Which brings us back to your original question—which you should now see just does not apply to G‑d: If we were talking about a human being, or an angel, or any sort of created being, we could ask, "So, how strong is it? Can it lift this? What about this?"—and we could measure that strength in those terms.
But when it comes to G‑d, none of this applies. If something is strong, or heavy, that comes from Him. If it can be lifted or not lifted, that also comes from Him. But none of this in any way measures who He is or what He is—since He is not measured by any qualities whatsoever.
Just to note: Some thinkers have asserted that this paradox proves that an omnipotent being is impossible. Yet mathematicians in the 20th century have come to accept that every system will of necessity contain some paradox. When your train of thought runs up against a paradox, it doesn't mean you're totally off track. It just means that there's a higher track, beyond your whole system of thought. That's the case here as well: This paradox is just a way of pointing out that the concept of G‑d lies outside and beyond our systems of logic.
I've provided a long-winded answer for the inquisitive mind. Sometimes, however, it's not a philosopher asking the question, it's just some smart-aleck. But the smart-aleck also deserves an answer. So you can simply say, "Sure G‑d can create a rock so heavy that even He cannot lift it. G‑d can do anything. And He could even lift that rock that He cannot lift as well."
That'll send 'em flying. And it's not untrue. Because it's simply saying that G‑d does not fit into any of our standard ways of thinking. G‑d is not a thing—He is the source of all things. The tools of measurement of things simply do not apply to Him.
Everything we learn or think about has to have some practical application. Here too, as well: Every day we pray to G‑d to heal the sick, feed the poor, knock sense into the politicians, and for all the other needs of humankind. Yet we preface all this by praising G‑d for being the ultimate in kindness and mercy and for being in complete control of all things. So if He is so kind and has so much control, why is the world such a mess that we have to ask Him to fix it up?
The answer is that G‑d created in the world a rock so heavy He cannot lift it. It's called our human free choice to make a mess of His world. And in our prayer, we ask that nevertheless, He should still pick it up. He should pick all of us up, and He will, as long as we pitch in just a little.