Something inherent is essential or inborn. An inherent trait for a human being is one that is essential to human nature.
Winston's initial rebellion comes out of a desire to express himself. He wants to assert himself on his own terms by writing in a diary, which seems a simple enough human desire. It also is an inherent human desire that cuts across time and cultures, as evidenced both by the art and stories all cultures produce and the difficulty totalitarian regimes have in stomping out human individuality. People across cultures, even in more rigidly conformist societies, want to have their identity and individuality acknowledged. People find it dehumanizing to be reduced, for example, from a name to a number or to have their name replaced with a different name. We all have an innate desire to own our own souls.
The regime in Oceania works hard to erase human individuality, trying to remake the inherent nature of humankind so that human bodies can be used solely for the purposes of the state. Part of the reason Winston can resist this so well is that he was born and spent a part of his childhood in the world that existed before the Party took over. The situation he lived in was desperately impoverished, but he grew up with a mother who loved him, in the context of an old-fashioned family situation. He can remember a time before the Party took over, and he has not been entirely brainwashed. He also is able to regain his humanity through entering into a loving relationship with Julia. All of this is what the Party wants to stomp out.
One of Orwell's working titles for the book was The Last Man in Europe. Winston is in many ways the last man because he is able to hang on, for a time, to his own identity and express his own thoughts and desires.