Sensitivity is determined by the lowest strength of a signal that a person will process consciously. It is related to, but not dependent on, sensitivity of perception. Two people may have the same hearing threshold or light sensitivity, but one of them may experience the same sound as more distinct, the same color as more lively, etc. So the same perception causes more activity in consciousness. This can be seen in fMRI images and EEG and EP curves. 
It is also important to distinguish sensitivity and sensitization. A person can be sensitized to some specific stimulus without being very sensitive in general. People are often sensitized to stimuli that bother them, like noise while trying to concentrate. After the noise reduces, sensitization causes them to be bothered even if the noise level sinks below their unsensitized threshold. In such situations the sufferer is often being called "sensitive", which contributes to sensitive people in general being perceived as "difficult".
A sensitive person is probably easier sensitized, but the similarities stop here. Being sensitized does not imply being very sensitive and highly sensitive people are not normally sensitized in an environment that does not flood them with stimuli beyond their sensitization threshold.
A person is highly sensitive, if they process stimuli in a way that is much more intense than experienced by the average person. If there was a reliable, standardized way to measure sensitivity, we would see the distribution of sensitivity form a bell curve. In this bell curve, "high sensitivity" would probably start at +2σ (two standard deviations above the mean), which would include about one out of 43 people. So if the press talks about "every 10th person being highly sensitive", they are probably talking about sensitization.
Traits of highly sensitive people typically include:
However, many highly sensitive people will try to cover up for their traits or even try to make a particularly tough and insensitive impression, because they are scared of their own sensitivity and consider it to be a problem rather than a gift. This strategy is probably predominant in men but, in a world that praises competition and recklessness, increasingly also found in women.
Unlike other mental traits, like high IQ, high sensitivity is not always considered to be a desirable trait, most probably because it is sometimes being associated with sensitization and hence equated with petulance. Even within the standard (±1σ), there can be discord: a rather insensitive guy (−1σ) might call a rather sensitive guy (+1σ) a "wuss" or a "lightweight". (Note that the distance between these two fictitious guys is the same as between the high-sensitivity threshold and the mean.)
On the other hand, where high sensitivity is considered to be a desirable trait, people who are not very sensitive are more likely to be regarded as highly sensitive, simply because they will claim to be so. People who actually are highly sensitive will usually be uncertain about the value of their trait, but a person within the standard will normally not have such doubts. Also, highly sensitive people are often overlooked or mistaken for being shy, because they are introverted.
So in the end, they often get the worst of two worlds: being identified as highly sensitive in one occasion and being blamed for it, and being overlooked in another situation, where the trait would actually be valued.
This is particularly sad, because this way nobody benefits from the gifts that highly sensitive persons have to give to the world: understanding, empathy, openness, sympathy, genuine interest, and so much more.
 For example, Jens Asendorpf has shown that the latency of evoked potentials is correlated with IQ.