Transitioning is the time period during which a person begins to live according to their gender identity, rather than the gender they were thought to be at birth. While not all transgender people transition, a great many do at some point in their lives.
Gender transition looks different for every person. Possible steps in a gender transition may or may not include changing your clothing, appearance, name, or the pronouns people use to refer to you (like "she," "he," or "they"). Some people are able to change their identification documents, like their driver's license or passport, to reflect their gender. And some people undergo hormone therapy or other medical procedures to change their physical characteristics and make their body better reflect the gender they know themselves to be.
Transitioning can help many transgender people lead healthy, fulfilling lives. No specific set of steps is necessary to "complete" a transition, it's a matter of what is right for each person. All transgender people are entitled to the same dignity and respect, regardless of which legal or medical steps they have taken.