The Transistor is the sword that was used by the Camerata to trace the consciousnesses of those they found helpful to their cause. The Transistor is the voice that is heard from it, and as Royce Bracket explains, it is normal for its wielder to hear the voices of those who dwell inside of it, but only the ones of the people that the wielder personally knows. Red carries along with her and enables her to interact with and destroy The Process, as it was once what controlled them. This ability was lost when it was removed from the Cradle for extended periods of time and then switched ownership from The Camerata to Red.
It was originally used by Royce Bracket to control the Process to build and demolish parts of Cloudbank according to what was voted on by the people. When he grew tired of this constant change, he allowed Grant Kendrell to use it for his cause to slow the change of their city, although they did not expect to lose ownership of it. It is apparently the only means of controlling or destroying The Process, as the assimilation of the town was essentially unhindered once they lost control of it. The Transistor may come from the neighboring reality that the Process themselves come from, and it may have been sent there by the Process itself as a means to jump from its own reality, which, according to Royce, it did not like, into the reality where Cloudbank existed.
Being traced into the Transistor is apparently a one-way street, and once inside, it is very difficult if not next to impossible to escape from. The only known way to remove oneself from the Transistor is to delete another competing consciousness that is attempting to leave from the Transistor as evidenced by Royce.
Red | The Process | The Transistor | Cloudbank | Sandbox | Backdoors | Locations | OVC Terminal | Junction Jan's | Access Points | Fairview | Camerata | The Story | The Country | The Spine of the World