Sperm fertilizes the egg and then it keeps dividing into more cells. Wait 9 months and you were born.

You mean fertilization? Egg and sperm cells are unique in that they carry half genomes, which conveniently make a whole one again when you put the two together. The sperm in this case contributes pretty much just that genetic information to make the egg complete.

The egg then goes on to multiply, and is therefore the common ancestor of every single cell that will ever be a part of you -- and your own descendants, if any.

Your mom's egg and your dad's sperm both contain half of the DNA it takes to make a person, including the DNA instructions it takes to run a living cell. Other cells have a whole copy.

Before that, those cells (egg and sperm) are supported by the body they come from, and their half copy of the DNA only has limited instructions for "running" the cell.

When the egg is "fertilized", the two half copiesf the DNA combine, finding their other half of the code, matching up, and arranging themselves into functional "genes". These genes contain instructions for just about everything; stuff that makes you related to your parents like hair color, etc, but also all the instructions for starting a human from that one cell.

There are instructions for cell division: how many, how fast, how much? .... Instructions for cell differentiation: how many of which kind of cell, where? Instructions on how cells arrange themselves: form a tube, or a ball, fold it in inward, you build this tissue, you build that tissue, you make heart muscle, you make a spinal cord, grow a spine with a tail, but then stop and re-absorb most of it!

After a while, you have a developing fetus that grows into a baby, if things go right.