The general definition of genre refers to any sort of communication (in any form) that is recognizable by social conventions that have developed over time. However, the use of genre most commonly refers to a system of categorization of forms of communication such as music, literature, art or entertainment.
The word genre was borrowed from French, where it simply means "kind" or "sort", which developed from the Latin genus, which meant "species", and is still used in Biological taxonomy.
The correct pronunciation of genre in English is szon-ruh. You will note that the pronunciation of genre in English basically mimics the French pronunciation. The "sz" is a phonetic transcription that represents the sound of the "s" in the word "vision". It is followed by a sound is pronounced similarly to the word "on". The last part, "re", is pronounced as -ruh, as heard in the audio pronunciation.