Baker's percentages are the ingredient measurements based on the weight of the flour (which is always 100%). For example if a dough formula calls for 16 oz. of flour (100%) and a hydration level of 50% the amount of water to use would be 8 oz. (by weight). The same holds true for all other ingredients.
The reason for using weights (as opposed to cups/tablespoons/teaspoons) is consistency. If you and I weigh 16 oz. of flour the amount of flour for each of us would be same because 16 oz. is 16 oz. However, if we each measure, say, 3 cups of flour the amount of flour could vary by several oz. depending on how each of us scoops and measures the cups.
Hope that helps.