I am a Brahmin, i always wonder when people keep asking what is the gothram that you keep talking about. I try explaining to them, about how we have a lineage. The roots from where we come from. Most of the times i find people staring at me blankly.....
so here is my research on the lineage

A Gotra is the lineage or clan assigned to a Hindu at birth. In most cases, the system is patrilineal and the gotra assigned is that of the person's father. Other names used to refer to it are Vansh, Vanshaj, Bedagu, Purvik, Purvajan, Pitru. An individual may decide to identify his lineage by a different gotra, or combination of gotras. For example Lord Rama was Surya Vansha, also known as Raghu Vansha. This was because Lord Rama's great-grandfather Raghu became famous.
The term gotra, itself, according to strict Hindu tradition is used only for the lineages of Brahmin, Kshatriya and Vysya families. A Gotra relates directly to the original seven or eight Rishis of the Vedas. In this sense, Lord Rama did not have a Gotra, and in rituals his Gotra would be the Gotra of his Brahmin priest. This practice is still common today as it was in ancient times according to earliest Hindu sources. Therefore, Gotra has always been only a Brahmin lineage that descends from seven or eight rishis associated with the Saptarishi or the seven stars of the Great Bear constellation as according to original Hindu Vedic system. The word "Gotra" means "ray." In Brahmin tradition, it is the duty of the Brahmin to keep his particular ray alive by doing daily rituals that he may transmit the power of that ray to others for the benefit of mankind. When the "ray" is extinguished, so is that particular beneficial magical stream dead to the human race and that power lost to mankind forever. Hence the importance of a Brahmin's daily Sandhya.
The Sanskrit term "Gotra" was initially used by the Vedic people for the identification of the lineages. Generally, these lineages mean patrilineal descent from the sages or rishis in Brahmins, warriors and administrators in Kshatriyas and ancestral trademen in Vaisyas.

Recently, the term "gotra" has taken broader meanings to include any lineage, Brahmin or otherwise. Therefore, today, other terms are considered synonymous with gotra and the distinct meaning of the word and the esoteric connotations are lost to many, even within the Brahmin community.

A common mistake is to consider gotra to be synonymous with clan or Kula. A kula is basically a set of people following similar rituals, often worshipping the same God (the Kula-Devata - the God of the clan). Kula has nothing to do with lineage or caste. In fact, it is possible to change one's Kula, based on his faith or ista devatha.
It is common practice in Hindu marriage to enquire about the Kula-Gotra meaning Clan-Lineage of the bride and bridegroom before approving the marriage. In almost all Hindu families, marriages within the same gotra are prohibited since people with same gotra/gothra are considered to be siblings. But marriage within the kula is allowed and even preferred.

Marriages and gotras

Marriages within the gotra ("swagotra" marriages) are banned under the rule of exogamy in the traditional matrimonial system. People within the gotra are regarded as kin and marrying such a person would be thought of as incest. In some communities, where gotra membership passed from father to children, marriages were allowed between uncle and niece, while such marriages were forbidden in matrilineal communities, like Malayalis and Tuluvas, where gotra membership was passed down from the mother. A much more common characteristic of south Indian Hindu society is permission of marriage between cross-cousins (children of brother and sister). Thus, a man is allowed to marry his maternal uncle's daughter or his paternal aunt's daughter but is not allowed to marry his father's brother's daughter, a parallel cousin, who is treated as a sister.

Hope i have cleared the doubts people have........I am Atherya one of the Sapta Rishis.......