[ETA: So does mlawski, in a more hilarious but equally thinky fashion.]
I think a lot of confusion comes from that description, just on the basis of the word "strong." It means a bajillion different things.
A "strong" character can be:
-a character with lots of physical (or magical or something) power
-a character with a well-defined and believable personality
-a character with a very forceful personality
-probably some other stuff that I can't think of now
A character that's one of these things isn't necessarily all of them. (I'd come up with examples, only I tend not to keep paying attention to stories that don't offer me #2 there, so yeah.)
The point is, a creator can create, say, Awesomegal, who is a superstrong superhero, only she has zilch in the way of personality and reads like someone's strawman*, and then feel shocked (SHOCKED!) when all these mean feminists say, "Dude this is not a Strong Female Character! You fail!" I mean, check her out, she is totally lifting up a TANK there, how is that not strong?
Alternately, we could have, say, Patheticia McWussmobile, who has no powers and gets chafed by the wind, but when she gets all caught up in the fact that her boyfriend is secretly involved in a secret war against secret alien conspiracies to secretly take over the world secretly, she doesn't run off and cry (or at least doesn't for very long) but instead offers whatever support she can- not just emotional but, say, research, or clipping important news stories, or being on the lookout for people who don't look very people-like- until she gets kidnapped, at which point she makes an effort to escape (even though boyfriend has to save her because it's apparently required in these stories). And what's more, she'll keep doing this support even if he, say, breaks up with her for that other girl on the Alien Fighting Team, because it's the Right Thing to Do, and Alien Invasions Suck.
Patheticia has almost no physical strength, but she's a strong character because she Does Things on her own, by her own will.
The two examples aren't mutually exclusive, either. There are a few female characters who're strong in all the senses I cited- can open cans of whoopass AND have personalities and Do Things. The point is, your female character doesn't have to be physically (or otherwise) powerful to be a Strong Female Character. Generally, when we mean feminists (or at least many of the ones I know) talk about a Strong Female Character, we're talking about someone who has a sense of self, who makes her own decisions, and who reads like an actual person. Whether or not she can punch through buildings is irrelevant.** Whether I, the reader, can identify with her... that's the most important thing.
*Let's assume that this was not actually the intent of the creator, and that Awesomegal isn't supposed to be some crazy parody/satire/other comedy.
**Though if she can, that's awesome, too. I like reading about gals that can punch through buildings.