The aim of this work is to introduce the reader into the problem of partitions. Gradually, on isolated examples of models of this concept, we show its importance in Mathematics. In conclusion, we formulate a sufficiently general definition of a partition, which then will no longer be only a formal knowledge of a student. The impulse to write this article were some mistakes in study materials published on the Internet by teachers of Mathematics. This article is intended for prospective teachers of Mathematics as well as their teachers.