A character profile for a Shakespearean character is, as has been said above, the same as for any character, and many of the components of a character profile are listed in that answer. I would add that a character profile for someone performing the role would, again, include all the above, plus a good deal more. In this case, it would also include the following: a. What are the character's most pressing needs and desires? b. What has the character been doing just prior to entering into the play for the first time? c. What does the character want to have happen as a whole, and moment to moment? d. What do they do to accomplish that? e. What has the character's life been like up to now and how does that affect how he behaves, speaks, moves, etc.? Actors are trained to create character profiles for the roles they play, the purpose of which is to become intimately familiar with the minutiae, as well as the larger events, of the character's life, thereby enabling the actor to incorporate this data into their performance.
It is very enriching for Shakespeare's readers, too, not just actors, to ask these questions about the characters, because answering them shifts the reader's attention onto a deeper level of understanding and enjoyment of the play.
The features of a character profile are the same for any character, Shakespearean or not.
An author will use a character profile to help "flesh out" a character and build them up. This will make the character more and more real until he or she seems to "come alive."
For a reader, a character profile asks all of the same questions that the author used to build that character, but a reader is deconstructing the character and breaking him or her into component parts.
A part of any character profile will be some basic statistics that include things like name, age, socioeconomic status, birth order, relationship, weight, height, skin color, etc. Let's apply that to Romeo. His name is Romeo, he's male, an only child, from a wealthy family, first in love with Rosaline then Juliet, he's skinny, of moderate height, and Caucasian.
Another part of the profile will include personality traits, intellectual ability, and emotional characteristics. So again for Romeo you could say that he is spontaneous, romantic, quick-witted, friendly, not close to his mom or dad, well educated (based on his wealth and punning ability), and prone to deep mood swings.
With a character broken down like this, it becomes easier to see how that character affects the overall events of a story.