Well intelligence is really some kind of property of learning. Maybe people who learn faster or better or something like that could be said to be more intelligent. We should translate this question into one about learning since it will be much easier to get a handle on that way.
We can distinguish a few different parts of any "learning machine".
1). There has to be a finite amount of data coming in from the outside world.
2). There has to be a set of assumptions about the way that the data is generated. This could take the form of an a priori probability distribution or some other similar notion.
3). There has to be a learning algorithm which generalizes from the data so as to be able to predict new data that has not yet arrived.
We can think of this like fitting a curve to data. Consider a finite set of data (x_i,y_i). We can pick a learning algorithm like "pick the line that minimizes the sum of the squares of error on the observed data". We use the assumptions in order to restrict the class of curves we consider. That is, perhaps we've assumed the data should all fall on a line then we only need to minimize error on the data for lines.
Such learning machines can generalize from observed data. In a deep sense, this is what we mean when we speak of intelligence. We say that someone who is more intelligent is better at generalizing from observed data to new situations.
So this implies that there could be a few reasons that one person is more intelligent than another. Perhaps the more intelligent seeming person just has a better set of assumptions about the world. If you are trying to learn the rule as to how data was generated by a Gaussian distribution but you refuse to entertain the possibility that the data was not generated by a Poisson distribution then no matter how much data you get, you'll never be able to generalize well. Similarly, incorrect prior assumptions about the world can impede human learning.
Another reason that someone could seem more intelligent could be that this person simply has more data. Learning machines always perform better when given more training data to work with. This could translate into a sensory issue, maybe some people merely notice more things in the world and thus appear to learn more easily/accurately.
Lastly, a person might have a better learning algorithm than someone else. Maybe one that converges faster or takes outliers into account in different ways. This is speculative, but it seems likely that the learning algorithms we use are probably hardwired into us by genetics.
Also it is certainly true that no learning algorithm is ever superior to others in every domain of application. So it is likely that if we really do have a person who is doing better at some task than other people because she has a better learning algorithm then this is probably task dependent. We could probably find other tasks where she does not excel in the same way.
