What does "back to school" mean? I'm not a native speaker and see
these three words pop up quite often, but I never quite know what it
means.

Dear j_philipp-ga;

Thank you for allowing me to answer your interesting question. In the
United States children are required by law to attend school. The
educational school year for children is typically about 9 months long.
The remaining three months represent a vacation period over the summer
months. When the summer vacation ends the new school year begins
(usually in August or so) and children begin returning to school as
the law requires. This period is unofficially, but commonly referred
to as ?Back To School? time.

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Tutuzdad-ga ? Google Answers Researcher

Apparently the "back to school" slogan has a long history in New Zealand, too:

"And for the last 300 years, advertising agencies have, at great cost,
advised their yawnie clients to use the orgasmic 'back to school'
slogan."

http://www.btob.co.nz/archives/bus_maverick/maverick03.htm

"To go back" means "to return."  So "back to school" is a short way of
referring to "GOING back to school."

In stores and store advertisements, you see "Back to School" signs and
labels on merchandise that can in some way be related to the start of
a new school year, such as clothing, backpacks, notebooks and
supplies, and lunch gear.  It is more of a merchandising gimmick than
anything else, the idea being that for a new school year you need to
buy a lot of stuff in preparation.  You don't really have to buy a lot
of stuff, but advertisers will use any device they can to motivate
sales.

Archae0pteryx