Often they have been aware of feeling trapped in the wrong kind of body since they were very young, and the process of altering their physical self to match their emotional self is tremendously liberating. This may sound obvious, but we need to remember that transsexual people are the gender that they have decided to be. In other words, a person who was born with a female body, who decides to become a man, is then male. A person who was born into a man's body and then decides to become a woman, is then female. But when we are aware that someone is making a specific choice about their gender identity, we should honor that.
People have the right to be self determining.
The second meaning of trans is across, as in transcontinental. Some transgender folks cross back and forth between genders. Maybe they are comfortable being male for the most part, but occasionally like to wear women's clothes. Maybe they have a female body and identify themself as male, but don't feel the need to change their body to move across that gender line. Cross-dressers would fit under this definition of trans.