Gotra means Clan esp. in Hindu society. It refers to people who are descendants in an unbroken male line from a common male ancestor.
Can I marry a person of same gotra?
According to Hindu religion, same-gotri marriages are prohibited. This prohibition is because they believe that the girl and the boy have common ancestors that is why they are like brother and sister. No one can marry her sister or vice versa. Gotra decides your lineage. If you are a Hindu then why are you thinking of marrying a person from same gotra. I hope you would not like to marry a girl who is your sister.
Scientifically, it has also been proved that marriage between persons having the same lineage produces babies having several genetic disorders and diseases. So science also believes the same way as Hindu Rishi Munis have written long before. Think how knowledgeable were our ancient Rishi. They were great biologists. They have told us long before what science is inventing today! (yahoo answer)
Gotrya can be identified with your surname. Below is the detail information about Gotra and surnames that includes. (source:-wikipedia)