a private bilingual primary school operating as an open, all-day school

"Offen" appear to mean non-compulsory attendance in the afternoon.

Offene Schule (OS) - ganztägige Schulform mit getrennter Abfolge von Unterrichts- und Betreuungsteil
(das heißt: Der nachmittägliche Betreuungsteil schließt an den Vormittagsunterricht an und besteht aus Freizeit incl. Mittagessen und täglicher Lernzeit). Die Anmeldung kann auch für einzelne Tage der Woche erfolgen und gilt jeweils für das laufende Schuljahr.
http://www.wien.gv.at/ssr/allgemeines/begriffe.htm#O

The Federal Government is promoting the development of so-called "open-all-day schools" which provide a non-compulsory afternoon programme, mainly with the help of voluntary teachers, such as parents, students, senior citizens and sports trainers. Unlike in many neighbouring countries, pupils in Germany normally only attend school in the morning, or at most until one or two o’clock in the afternoon. There are a few exceptions within the state school system, which have lessons until four o’clock in the afternoon. The hope is that this will give greater equality of opportunity to children from "underprivileged" backgrounds who are given little encouragement to learn at home. Such opportunities are used by just ten per cent of all children in compulsory education (up to the age of 16).

http://www.goethe.de/wis/sub/thm/pan/en116181.htm

A school is considered an all-day school, if in addition to the morning lessons it offers an all-day option for students on at least three days a week. This encompasses at least 7 full hours every day, a lunch break, and supervised afternoon activities organized by the school administration.13 The afternoon program is not compulsory for students and its personnel are not necessarily recruited from the teaching staff. It neither changes the actual amount of time of school instruction (timetable) nor the curriculum.

Generally, not all of the students of a school attend the afternoon program.
For the most part, the afternoon is made up of doing homework, taking part in extra-curricular activities and playtime (no teaching). Pedagogical staff who are not teachers and whose qualifications vary greatly primarily supervises these.

http://www.ph-ludwigsburg.de/html/9e-aaax-s-01/seiten/Sympos...