A paternity test is conducted to find out who is the baby's daddy, whether a man is the biological father of another individual. This may be important to show duties of the father. Similarly, a maternity test can be carried out. This is less common, because at least during childbirth, except in the case of a pregnancy involving embryo transfer or egg donation, it is obvious who the mother is.
DNA has all but taken over all the other, older forms of paternity testing. The DNA of an individual is almost exactly the same in each and every somatic cell. Sexual reproduction brings the DNA of both parents together randomly to create a unique combination of genetic material in a new cell, so the genetic material of an individual is derived from the genetic material of their parents. This genetic material is known as the nuclear genome of the individual, because it is found in the nucleus.
Comparing the DNA sequence of an individual to that of another individual can show if one of them was derived from the other or not. Specific sequences are usually looked at to see if they were copied verbatim from one of the individuals genome to the other. If that was the case, then this proves that the genetic material of one individual was derived from that of the other (i.e.: one is the parent of the other). Besides the nuclear DNA in the nucleus, the mitochondria in the cells also have their own genetic material termed the mitochondrial genome. Mitochondrial DNA comes only from the mother, without any shuffling.
Proving a relationship based on comparison of the mitochondrial genome is much easier than that based on the nuclear genome. However, testing the mitochondrial genome can only prove if two individuals are related by common descent through maternal lines only from a common ancestor and is thus of limited value (for instance, it could not be used to test for paternity).
Obtaining news that a child either is or isn't one's own is something that a parent or erstwhile parent can undertake at their own expense, without necessarily informing anyone either about the test or its result. However this situation will change when the Human Tissue Act comes into force in the UK in April 2006. Section 45 states that it will be an offence to possess any bodily material intending that any human DNA in the material be analysed without qualifying consent
Tests can also be ordered by courts when proof of paternity is required.
A wide variety of genetic studies appears to show that the rates of non-paternity in the general population are much smaller than this, of the order of 4% [1] to over 30%, depending on the social group involved; having said which, these rates may still surprise many people.
Some information excerpted from wikipedia