A mitzvah is a commandment, one of the divine imperatives that constitute the covenant obligation of Jews. Rabbinic tradition counts 613 of them: 248 positive and 365 negative, a figure attributed to R. Simlai in the Talmud (Makkot 23b). The enumeration itself came later and was disputed; Maimonides' Sefer ha-Mitzvot produced the list that became standard, and Nahmanides' critique of its governing principles is the most substantial disagreement with it.
Several classical distinctions organise the field. Commandments between a person and God are distinguished from those between a person and their fellow, and the difference is practical: the second kind are not forgiven on the Day of Atonement until the wronged party has been appeased. Commandments for which reasons can be given, mishpatim, are distinguished from those for which none is apparent, hukkim, the red heifer and much of the dietary law being the standing examples. Whether reasons should be sought at all was itself contested, Maimonides arguing at length in the Guide that every commandment has an intelligible purpose, and others holding that obedience without a reason is the purer service precisely because nothing but the command motivates it.
The seven Noahide commandments are held to bind all humanity, and this has an important consequence for Judaism's posture toward other peoples: righteousness does not require conversion, and the tradition's standard position is that the righteous of the nations have a share in the world to come. Judaism accordingly developed neither a general missionary imperative nor a doctrine that salvation requires membership.
In ordinary modern speech the word has drifted, and mitzvah now commonly means a good deed or an act of kindness, a usage that is the more familiar one outside observant circles and that the tradition's own emphasis on the commandments between people made easy. The Bar and Bat Mitzvah, "son" and "daughter of the commandment", marks the age at which a young person becomes obligated; the ceremony recognises the obligation rather than conferring it, and the obligation arrives whether or not any ceremony is held.