A Jewish person is a person that believes in the God of Abraham but dies not believe Jesus was the Messiah nor that Mohammad was a prophet. There is certain cultural aspects that go along with the Jewish religion and people who aren't religious participate in this same culture.
Jewish is a religion. There us no such thing as an atheist Jew anymore than an atheist Muslim or Christian.
That is my opinion anyway.
Mostly true, those who belong to actual tribe can be Jews without belonging to the religion.