Your child is not only mobile, she's skilled at jumping, hopping on one foot, pedaling a tricycle, alternating feet on stairs, and dressing herself (sort of).  If these things aren't happening independently, they likely will soon.

She should become more conscious of herself.  For instance, know and communicate when she's thirsty, hungry, cold, hot or tired.  Her speech should be mostly understandable and she should know most colors, and maybe even count to ten.

Your child should be able to feed herself by now.  Her portions however, are not the same as yours.  Three tablespoons of food equals a serving at this age.  You should avoid giving your child junk food, soda and fast food.  Juice should contain no added sugar and should be limited to 4-6 ounces per day.  If your child is used to drinking more juice, try watering it down a little bit at a time until she is drinking mostly water.

Your afternoon break may be a thing of the past.  Naps are hit or miss at age three and your child will likely give them up altogether very soon.  Having a regular bedtime and routine leading up to lights out, will help your child feel confident and safe.

At age three, your child should be using the toilet and remaining dry most of the day and some nights.  Never punish your child for accidents.  Praise her when she remains dry, especially overnight.