The sperm and the egg each contain 1/2 of the genetic material needed. Physically the egg is much bigger, but the important contribution of each is the genetic information. On their own, neither an egg nor a sperm is a baby. They have the potential to form a baby if the sperm reaches the egg and can fertilize it before another sperm gets through the cell membrane of the egg. In a typical fertilization situation, you have a bunch of sperm getting nowhere near the egg, a small percentage getting to the egg, and one that manages to get through the cell membrane to fertilize the egg. Once fertilized, the egg has a complete human genome, a unique set of its very own DNA which has the plans for the entire unique adult person it will become.
(Technically the egg actually also contributes all of the mRNA, but this is really a very minor point that has to do with organelles.)