We are commanded to study Torah and to teach it. This will enable us to keep the mitzvos and to raise children who are able to do likewise. In this context, “children” isn’t limited to biological children, it includes students. (Refer to 2 Kings 2:3, where the prophets’ students are referred to as “sons of the prophets.” Similarly, see Rashi on Numbers 3:1, where Moshe was considered a parent to Aharon’s sons because he taught them Torah.)
A person is obligated to teach his child Torah from the time the child is able to speak. We begin with simple Bible verses until the child is old enough to enroll in school. If a person’s father did not teach him Torah when he was young, he is obligated to go out and learn it himself when he is old enough to do so. The obligation to learn is ongoing, lasting a person’s entire life.
The obligation to study Torah applies to everyone, rich and poor. The Talmud in Yoma (35b) tells us of Rabbi Elazar ben Charsom, who was a great captain of industry, and of Hillel, who froze himself on a rooftop so he could listen in at the yeshiva’s skylight. Both of these men were great scholars. Rabbi Elazar studied Torah even though it meant neglecting his business, while Hillel studied Torah even though he could have used the time to make a living. Either way, financial status is not an excuse to shirk Torah study.
The reason for this mitzvah is that learning Torah elevates a person. It not only arms a person with the tools needed to keep the mitzvos properly, it draws us closer to God. (As we said in the previous mitzvah, the more we get to know God, the closer we get to him.)
This mitzvah applies in all times and places; only men are obligated per se but obviously women also learn and teach Torah. In the Talmud, this mitzvah is discussed in tractate Yoma (35b) and Shabbos (119b), among other places. It is codified in the Mishneh Torah in Hilchos Talmud Torah. It is #11 of the 248 positive mitzvos in the Rambam’s Sefer HaMitzvos and #14 of the 77 positive mitzvos that can be fulfilled today as listed in the Chofetz Chaim’s Sefer HaMitzvos HaKatzar.