"Your worst enemy, he reflected, was your own nervous system" reflects an essential irony in 1984 and also a central theme of the book, betrayal.
Winston's worst enemy was the state, in the form of Big Brother. It is Big Brother who controls not just every physical aspect of Winston's life, but even his psychology and sense of history. The whole point of newspeak is to reduce the possibility of dissent through limiting the language available to the people. Ironically, in his resistance to Big Brother, Winston has to deal with the fact that the human nervous system reveals the existence of undesirable thoughts and makes it impossible to hide his resistance. He might intellectually resist Big Brother, but his body becomes a betraying enemy as he does so.
The political system represented in 1984 is based on mutual betrayal. A major way of keeping people under control is to make sure they can trust no other human being. Winston tries to avoid betraying Julia, but he ultimately fails. The antique shop owner and O'Brien take a more cynical approach to betrayal through being agents of the state and lying to Winston. No characters in the story are able to find their way out of this insidious system.
Winston says this in narration when describing the Thought Police. He was almost describing how thoughts can be read because it is humanly impossible. the Thought Police had to use any little glitch of gesture to determine if people were actually demonstrating guilt in their actions as a result of their thoughts.
The human nervous system is what contols and manipulates even the most involuntary gestures. These gestures might come as a result of an emotion or feeling like guilt or pleasure. If a Party member was not in complete control of their nervous system, they could unintentionally give the Thought Police the idea that they were having thoughts that they were not supposed to have.