Why are some people Jews?

Answer 1

Jewish tradition states that a Jew is any person whose mother was Jewish (Talmud, Kidushin 68b), or any person who has gone through a proper conversion to Judaism (Talmud, Yevamot 47a).
The word "Jew" (in Hebrew, "Yehudi") is derived from the name of Judah, the fourth son of Jacob and one of the Twelve Tribes of the Israelites. After the Ten Tribes went lost some 2600 years ago, the Tribe of Judah constituted the majority of the remaining Israelites; so since then we have simply been called "Jews" (people of Judah), even for those of us who may be from the other Israelite tribes.

What does Judaism give us?

1) An identity and tradition. Jews have an unbroken tradition stretching back for 3800 years to our founder, Abraham. We possess the exact same text of the Torah that God gave to Moses over 3300 years ago. We have the names, dates, and teachings of the leading sages in every generation since Abraham.

See: Jewish history timeline

2) A life. Some might consider the laws of Judaism as being too much, but for us they are a life, with happy festivals, structured family life, daily activities, and a sense of purpose. Judaism is famous for its ambiance and its optimism.

See: The Jewish holidays

3) Community; friends. Every Jewish community has individuals and groups who give free help in loans of money or useful items, visiting the sick, preparing the dead for burial, assisting young mothers, etc. This is done voluntarily and is not for profit.

Jewish communities have free daily and weekly classes in Torah-subjects, both in synagogues and in other public and home-venues. In these settings, laypersons can ask questions in topics such as halakha (Torah-laws) and Talmud.

4) Eternity.

Rabbi Jacob Emden (1697-1776) once said that the survival of the Jewish people is the greatest of miracles. It can be explained only as a fulfillment of God's covenant.
Consider also this famous quote from Mark Twain:
"If the statistics are right, the Jews constitute but one quarter of one percent of the human race. The Jew ought hardly to be heard of; but he is heard of, has always been heard of.
The Egyptians, the Babylonians and the Persians rose, filled the planet with sound and splendor, then faded to dream-stuff and passed away; the Greeks and Romans followed and made a vast noise, and they were gone; other people have sprung up and held their torch high for a time but it burned out, and they sit in twilight now, or have vanished. The Jew saw them all, survived them all, and is now what he always was, exhibiting no dulling of his alert mind. All things are mortal but the Jews; all other forces pass, but he remains. What is the secret of his immortality?"

Answer 2

Functionally
Any person born to a Jewish mother OR who converts to Judaism BUT does not convert out of Judaism to a different religion (Christianity, Islam, etc.) is a Jew. (Jews who "deconvert" to Atheism are still considered Jews.)

Value of Being Jewish
There is a common saying among Jews that having two Jews yields three opinions, since Jews rarely agree on anything. As a result, I will put my views below and the fourteen million others of us may be free to join in on what they value about being Jews.

Firstly, being Jewish means being granted a front-row seat to a tradition that has existed for over three thousand years, its festivals and its feasts, its celebrations and its calamities. It means being a part of civilization that witnessed numerous proud and noble empires rise and fall, outliving all of them, as well as building its own states subject to the same laws. It means being part of a select group that has inordinately contributed to the strength and vitality of the human endeavor. It means being part of a community that values both reason and faith as pillars of wisdom and direction. It is being among people who seek to determine ways in which we can benefit the world, rebuilding it by the strength of our hands, the love in our hearts, and faith in our Creator. Jews are the perpetual Others, gifted with the unique ability to comment on the rest of the world and serving as a litmus test of decency or travesty, critiquing the successes and failures of other civilizations in their greatest heights and lowest improprieties. I also see a community that encourages dissent and disagreement without supporting discord or chaos, enshrining religious disagreements along with its sacred texts. Being Jewish means being a member of a group that values dissent as a way of reaching a better and more developed truth, rather than a form of insubordination.

Answer 3

I am a Jew because my mother is Jewish and since Judaism is a ethnoreligious nation/people you need to be born into it, but we also welcome converts.