Before reading about reproductive system problems, it is helpful to understand how the reproductive system works, part of which includes egg laying.
A hen's reproductive system consists of two parts: the ovary and the oviduct. The ovary contains thousands of ova (see the diagram below) which can develop into the yolk and eventually an egg. A hen therefore has the ova of every egg she can ever lay inside her body.
An ova is placed into a yolk and when it reaches its final size, it breaks away from the ovary. This process is called ovulation. All eggs contain an ova and it is possible to see this in the yolk when you open an egg - it is called the germinal disc. The yolk enters the oviduct where the albumen (white) and the shell are added. Most female animals have two active ovaries and oviducts but hens only have one. The left ovary and oviduct is functional but the right ovary and oviduct are dormant. When a cock mates with a hen, he will deposit semen that will go into the oviduct and as the yolk passes through, the semen connects with the germinal disc (ova) and becomes fertilised.
The ovulation period of a hen is 24 to 26 hours so she will normally lay later every day. Hens in lay will lay an egg each day for about six or seven days. This group of eggs is known as a clutch. A clutch of eggs is followed by one or more days when the hen doesn't produce an egg. In practice, there are many factors that affect laying.
The process of egg laying is triggered by hormones in a hen's body. The pituitary gland in her eye produces these hormones when it is stimulated by light. Chickens generally need about 14 - 16 hours of light per day to come into lay and (in the UK) will usually stop laying between November and January.
It is not possible to see with the naked eye whether an egg is fertile or not until it is incubated when it can be candled (usually after a week) and the spider like development of blood vessels can be seen.