What does it mean to a Jewish person to be Jewish?

Answer 1

It depends on how the question is read. It could be read to be asking: (1) What is the definition of being a Jew, or (2) what does being a Jew mean to the Jew, i.e. its value.

1) Definition of Being a Jew: Judaism is the religion and way of life of the Jews. Judaism began as recorded in the Torah, and is expounded upon in later sources such as the Talmud. Judaism is the expression of the covenantal relationship which God created with the Israelites (Exodus ch.19). God revealed his laws and commandments to Moses (Exodus 24:12) in the Written and the Oral Torah. Judaism possesses a historical continuity overmore than 3300 years. It is one of the oldest monotheistic religions, and the oldest to survive into the present day. Many aspects of Judaism have also directly or indirectly influenced Western ethics and civil law.
Jews are an ethno-religious group that includes people who were born Jewish as well as converts to Judaism.

Orthodox Judaism maintains that the Torah and Jewish law are Divine in origin, eternal and unalterable, and that they should be strictly followed. Historically, special courts (Sanhedrin) enforced Jewish law; today, these courts (Batei Din) still exist but the practice of Judaism is voluntary. Authority on theological and legal matters is vested in the Jewish texts and the many rabbis and scholars who interpret them.
See also the Related Question:
What are the key teachings practices principles and beliefs of Judaism?

2) Value of Being a Jew
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 2

According to Halacha (Jewish Law) to be a Jewish person one must either be born of a Jewish mother or have formally joined the Jewish people. For a non-Jew to formally join the Jewish people (Geirut), both men and women must learn about Judaism and accept its laws, and then appear before a Beit Din (Rabbinical tribunal) and undergo a Mikvah (full immersion in "Living" waters). Additionally a male who is uncircumcised undergoes a Brit Milah (Halachic Circumcision) and a male who was medically circumcised must go through a Hatafat Dam Brit (ritual circumcision involving a tiny incision near the glans).

A person whose father is Jewish and mother is a non-Jew is not Jewish.

A person who was born a non-Jew and has not completed all of the steps required for Geirut is not Jewish.

Answer:For a Jewish person, being Jewish is an identity, a community, a lifestyle and a set of beliefs, morals, attitudes and observances. These include the attitudes/beliefs that life is precious, meaningful and important, the world isn't a free-for-all, God is infinitely wise and kind, our free-will is a gift which must be carefully and responsibly used, and our soul and relationship with God must be nurtured through prayer, observance of the Torah and living according to its ways.