A character sketch is a very important element of writing that uses techniques of description, narration, and exposition to convey an idea of the kind of person the subject is. It differs from a biographical sketch in that the primary focus is revealing interesting or important aspects of personality and character, rather than describing interesting or important events in the subject's life. Here is a real, honest-to-God, life example, taken from F. Scott Fitzgerald's This Side of Paradise*:
But Beatrice Blaine! There was a woman! Early pictures taken on her father's estate at Lake Geneva, Wisconsin, or in Rome at the Sacred Heart Convent--an educational extravagance that in her youth was only for the daughters of the exceptionally wealthy--showed the exquisite delicacy of her features, the consummate art and simplicity of her clothes. A brilliant education she had--her youth passed in renaissance glory, she was versed in the latest gossip of the Older Roman Families; known by name as a fabulously wealthy American girl to Cardinal Vitori and Queen Margherita and more subtle celebrities that one must have had some cultue even to have heard of. She learned in England to prefer whiskey and soda to wine, and her small talk was broadened in two senses during a winter in Vienna. All in all Beatrice O'Hara absorbed the kind of education that will be quite impossible ever again; a tutelage measured by the number of things could be contemptuous and charming about; a culture rich in all arts and traditions, barren of all ideas, in the last of thoise days when the greater gardener clipped the inferior roses to produce one perfect bud.
This passage above demonstrates the ambiguity of the line between character sketch and biographical sketch. But it is illustrating the character of Mrs. Blaine through a description of her education and social context; nurture and nature, after all. The emphasis is not on the education itself, but the effect. Here is another sketch (from the same book, forgive me, it's summer, I'm away from home and short of sources); it is easier to distinguish from a biographical sketch, and happens to describe a fictional girl I'd mind very little sharing half a raincoat with atop a soaking haystack in the middle of a Summer rainstorm...
Suddenly the lightning flashed in with a leap of over-reaching light and he saw Eleanor, and looked for the first time into those eyes of hers. Oh, she was magnificent--pale skin, the color of marble in starlight, slender brows, and eyes that glittered green as emeralds in the blinding glare. She was a witch, of perhaps nineteen, he judged, alert and dreamy and with the tell-tale white line over her upper lip that was a weakness and a delight. He sank back with a gasp against the wall of hay.
"Now you've seen me," she said calmly, "and I suppose you're about to say that my green eyes are burning into your brain."
*This entire book might be thought of one extended character sketch, of the principle character, Amory Blaine. Reading it may deepen your understanding of the idea of character development as a whole. On a slightly, no, totally unrelated note: I can't decide if I would like my child to be named 'Amory.'