When people talk about inside, they usually mean some internal information or knowledge that is not available to the general public. This can be, for example, data about a company's plans or personal opinions of a famous person that have not been officially disclosed. Inside is a kind of peek behind the curtain, where you can learn hidden details.
As for how to write it correctly — insight or inside — both options are used, but in Ukrainian, insight is more commonly encountered. If you look at the translation of inside into Ukrainian, it would be всередині, but in the context of inside, it simply means penetrating the essence of things. Insides are often valued for allowing an understanding of hidden mechanisms or predicting the development of events.