This is the 16568th most frequent Russian word.
своеобразная
Unique; distinctive; peculiar.
The word 'своеобразную' is used as an adjective to describe 'структуру', indicating that the structure is unique or unusual in some way.
Эта книга имеет своеобразную структуру.
This book has a peculiar structure.
The word 'своеобразной' describes 'атмосфере', pointing out that the atmosphere was distinct and special to that particular context.
Наша встреча прошла в своей своеобразной атмосфере.
Our meeting took place in its own peculiar atmosphere.
The word 'своеобразную' is used to characterize 'музыку', to note that the music has its own unique style or qualities.