The mould is no doubt from the residues of the soap used to shower. This would contain dirt, skin oils and fat that the soap has removed. If the curtain is then drawn to one side and left to drip dry this would be ideal "damp" conditions for bacteria to bread leading to mildew and mould.
To clean the curtain and prevent the mould from returning, try , once a month removing the curtain and washing it in the washing machine with say, half a mug of bleach with some white towels for ballast.
Immediately after showering, allow the curtain to remain across the bath to dry - this will help.