Chickens -- like other birds -- fertilize eggs via sexual reproduction. A hen will lay an egg at least every other day starting at about three months of age, but the eggs will only yield chicks if the hen mates with a rooster. Most production-oriented farms don't have a rooster milling about, unless it's time to make a new batch of egg-laying hens.
The Rooster Does His Part
In natural conditions, chickens will breed when the days begin to get long in spring. Males have reproductive organs not unlike mammals, with testes that produce sperm. The sperm travel down tubes called vas deferens to sperm sacs. During mating -- an unceremonious affair that lasts less than 30 seconds -- the sperm leave the male through an opening called a cloaca, and enter the female through an entrance to her reproductive tract, called the oviduct. From there, the sperm make their journey through the reproductive organs of the female. In a trip that may take a week or more, they swim through the hen's shell gland, then a narrowing in her reproductive tract called the isthmus, followed by the magnum and the infundibulum. There, they await the arrival of eggs in the process of forming.
Then the Hen Does Hers
A hen's eggs begin as yolks in the ovary, and once released they pass into the infundibulum, a funnel-shaped organ where the sperm are waiting. There they are fertilized, and pass out of the chicken via the same route the sperm entered. The egg white gathers around the yolk in the magnum. In the isthmus, the shell membranes are laid down. The shell forms and hardens in the shell gland, and the egg is ready to be laid. Most hens won't lay eggs in the evening, so if a hen's egg is ready then, she will likely hold it until morning. Once she does lay, she's ready to start forming a new egg. After mating, enough sperm may remain in the hen to fertilize her eggs for a week or more.