How important is the creaming process while making a cake?
The purpose mixing the butter and sugar until creamy is to distribute air through the batter that will help leaven the cake in the oven. Skipping this step can create a denser cake.   You want to add the air into the batter before adding the flour in order to prevent over mixing, which creates gluten; causing a tougher texture. 

Beating the eggs until foamy and folding them into the batter or adding the eggs to the butter/sugar and beating until fluffy will also create a lighter texture. 

The sugar does not need to dissolve in the butter, but it should be evenly distributed. This site gives a good visual on how creamed butter &amp; sugar should look.