Regarding Haters' FALSE "quote" of that case (Sanhedrin) attempting to paint
a false impression as IF 'marrying a 3 year old is ok'...
It is the manner of the Talmud to examine extreme theoretical cases in order to precisely define and delineate legal concepts. Such study is mandated because the laws are part of the Written and Oral Torah, not necessarily because they have practical application.
There are different legal consequences arising from an act of intercourse (related to personal status, punishment for rape, property rights etc.) and the Talmud investigates whether such an act committed on a baby girl has the status of intercourse or not. There is an ancient tradition that states that if the girl is older than the age of three then an act of intercourse was committed; before that age, such an act does not have the status of sexual intercourse for legal purposes (it may be an act of assault, of course).
The passage in question states as follows: "A girl of three years and a day is [capable of being] married by an act of intercourse ..." and the Talmud continues to list further legal consequences of an act of intercourse (laws of personal status, property etc.).
The reference to marriage refers to a case in which the father of the girl delivers his daughter to a man with the intention that he create a marriage bond with his daughter by having relations with her. >From a legal point of view this procedure creates a marriage with all the legal consequences that flow therefrom. This is a legal conclusion which has nothing to do with rabbinic endorsement of such practices or with the number of such occurrences in history.
In fact the rabbis strongly opposed formation of the marriage bond by intercourse (at any age) and punished those who acted in such manner (Kidushin 12b). They further taught that the father's right to marry off his daughter was to be used for her benefit. The age and manner of marriage is to a large extent a societal variable but at Kidushin 41a the rabbis taught: "It is forbidden for a man to betroth his daughter while she is young [but rather he should wait] till she has grown and says 'This is the one I want [to marry]" and this teaching is repeated elsewhere in the Talmud.
Copied from Philip Mathews of the Nizkor Project
Talmud does NOT Permit Pedophilia, Of Course!
The Truth about the Holy Great Beautiful Talmud Talmud = Peace