Transvestites (also called cross-dressers) are people who choose to wear clothes which are associated with a different gender identity to their own. This typically means a man (by sex)who dresses in feminine clothes, or a woman (by sex) who dresses in masculine clothes. Although this can include dressing androgynously and wearing both "men's" and "women's" clothes.
In the modern day, most transvestites are not transgender and do not want to transition. However, the concept of transvestites pre-dates widespread use of the term transgender, so in the past cross-dressing (particularly drag) was seen as a way for transgender people to express their identity. In these times, the two terms were often used interchangeably.