They are the Torah's laws (singuklar: mitzvah). Religious Jews live by the laws of Moses, by obeying these commands. There are hundreds of examples.
The laws themselves have various reasons. Some (such as the Passover) serve to reenact or remember events of our history.
Some (such as saying the Shema prayer) serve to reiterate our belief in God.
Some of the laws (such as those of ritual purity and kosher food) serve to sanctify us.
Some (such as the laws of torts) serve to maintain an orderly society.
Some (such as the law against breaking a vow) serve to prevent bad character traits.
Some (such as the command to offer help) serve to engender good character traits.
And all of the commands serve to subjugate us to God's will (especially those commands for which no explanation is easily apparent).
A few of the commands are:
Putting on Tefillin (a.k.a. phylacteries) in the morning
The sukkah-booth during Sukkot
Avoiding leavened products in Passover
Not eating on Yom Kippur
Not working on Saturday (Sabbath)
Paying workers on time
Marital rights for one's wife
Counting the days of the Omer
Returning lost objects when feasible
Wearing the tzitzith-garment
Learning Torah
Marrying and having children
Educating one's children in Judaism
Giving tzedakah (charity)
Honoring one's parents
And many more. Note that the Mosaic law "as is" isn't exactly what Judaism observes. Rather, It's the Mosaic law together with the details provided in the Talmud, which is the Oral Law that was handed down together with the laws of Moses (the Torah). Otherwise, the verses of the Torah are often too brief (lacking detail) to be fulfilled as is.
Mitzvah (plural: mitzvot) means commandments. It also colloquially refers to any good deed, though this is an incorrect usage of the word.
Ethical mitzvot deal primarily with relationships between people. For example, "do not steal" or "love your neighbor as yourself." You can contrast them with ritual mitzvot such as "do not mix linen and wool" or "do not eat swans." Some mitzvot are hard to classify; consider "do not harness an ox to a donkey" which seems just as ritual as not mixing linen and wool until you realize that an ox might weigh 4 times as much as a donkey, and it would be quite cruel to harness them together in a way that divides the load evenly between them.
commandment = mitzvah (מצווה) commandments = mitzvot (מצוות)
mitzvot = מִצְווֹת
Tradition holds that there are 613 guidelines by which Jews are to live, the Hebrew word for these guidelines is 'mitzvah' (singular) | 'mitzvot' (plural).
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