The word "gotra" means "lineage" in the Sanskrit language. Among those of the Brahmin caste, gotras are reckoned patrilineally. Each gotra takes the name of a famous Rishi or sage who was the patrilineal forebearer of that clan. And each Gotra is addressed by the suffix 'sa' or 'asa' as relevant.
The concept of Gotra was the first attempt among Brahmins to classify themselves among different groups. At the beginning, these gentes identified themselves by the names of various rishis (Angirasa, Atri, Gautam, Kashyapa, Bhrigu, Vasistha, Kutsa,and Bharadwaja; the first seven of these are often enumerated as Saptarishis). It is to be noted that Vishwamitra was initially a Kshatriya king, who later chose and rose to become an ascetic rishi. Hence the gotra was applied to the grouping stemming from one of these rishis as his descendants.

Though they are a minor exceptions,and that too at the advice of Panchangakartas, religious Heads, still a majority of the people are following the gotra ...more

I don't know and I don't believe in it either...!

I am in Kailasa gotra.it is relevant only at the time of marriage.