纸 is paper, 包 is wrap (the same bao for buns and bags), so 纸包 is paper-wrapped. 蛋 is egg, and 糕 is cake, thus 蛋糕 is egg cake, or in other words, a real cake batter type of cake, so altogether 纸包蛋糕 is paper-wrapped egg cake.
About This Dish
Paper-wrapped cake is a muffin-like cake common in Hong Kong and Chinatown bakeries, baked in a paper wrapping. Sometimes called paper-wrapped sponge cake or just sponge cake or cupcake.