The wearing of clothing that is for a different gender, than the person wearing it is.
Where a person will wear clothing specially for the other gender. A male for example, wearing a dress or lingerie specifically made for a female, or a female wearing jockey shorts, that are really made for males to wear.
Cross Dressing does not imply a person's sexuality, or desire for being a different gender. It is more of an action, than having any motive assigned to those who cross dress.
Bit cloudy, because terms such as homosexual, transvestite, transsexual, were not terms used in Ancient History, so it can't be certain as to whether those historic figures dressed in other gender clothing simply for comfort, or for other reasons.
There are many mythical references to where the Gods, or other mythical figures, cross dressed. Greek, Norse, all have such references.
Achilles is claimed to have dressed as a female when attending the Court of Lycomedes. Thor, the God of Thunder, is alleged to have clothed himself as a female, to regain the affections of another.
There are many reasons for cross dressing, many notable one's in History are of women donning male clothing to serve in the Military, to be with their male siblings, parent.
Historical examples exist, or are explained, in that in those times, women had very defined roles and status in society, denied many of the pleasures, responsibilities, associated with the Male's role.
Laws as well, defined what a female could or could not do, such as performing in Theaters. Hence males would assume the female roles, dressing accordingly.
History (Legend): The Legend of Pope Joan is one example of cross dressing. While many believe it is a myth, others claimed that she ruled as Pope from 855 to 858.
There are many ways to cross dress. Most easily identified is males who will wear female clothing, such as dresses, while it is harder to distinguish among female cross dressers.
Wearing certain undergarments, that are associated with use by the other gender would make a person a cross dresser.
Many people wear other gender underwear, hidden, so as to avoid being labeled as different. This can be a simple clothing fetish, not sexual in nature.
Practice (Associated Acts): In theater and stage, many troupes do not have sufficient women to play all the roles, so many male actors will don female garb, to play the roles.
Noteworthy: Drag Queens are performers who cross dress. The fact that they dress in garish outfits, or exaggerated styles does not imply their sexuality, though they are more common in Gay Clubs.
Cross Dressing can also be a form of rebellion against society, and its rules. It can be noted, that many of the instances in history are where woman dressed as men, in order to not be denied certain privileges only available to males, at that time.
The movie Yentl, with Barbara Streisand is such an example, where she dresses, acts like a man, in order to gain religious teachings, not allowed for women, at that time.
In some cultures today, that still exists, most notably the Muslim Nations, such as Iran or even Saudi Arabia.
Cross Dressing is listed as an 'abomination' in the Bible (Deuteronomy 22:5), despite the so called Holy Transvestites (Saints who were women, but dressed as men).
Cross Dressing can be for comfort, for a desire that does not involve any sexual preference. Simply put, a man dressing in woman's clothing does not make them want to be a woman, or have sex like a woman.
Other associated reasons for cross dressing, is hide their true identity, for fear of persecution, for denial of some feature of local society. Saint Mary of Alexandria for example, joined a monastery with her father, an act not allowed at that time, and only upon her death, was it discovered that she, was a she. In fact, during her life, she had been accused of getting a female pregnant, but refused to reveal her sexual gender, even under those circumstances.
In History and Modern times, men have dressed in female garb, to avoid conscription, or to imply a sexuality that wasn't existent.
Television shows, such as MASH, have used this for comical relief, as in the character Klinger in that show.