Ford term for an early emissions control system, installed on cars from around 1965; by 1967, California specification vehicles were installed with it as standard. The name is a contraction of 'Thermal Reactor', and this type of system is also known as AIR (air injection reaction).
The purpose of the Thermactor system is to reduce the emission of unburned fuel and the products of incomplete combustion. It does this by injecting air into the exhaust manifolds; the heat of the exhaust gases is sufficient to ignite the combustion of anything burnable still remaining in the exhaust. The combustible gases, mixed with oxygen from the injected air, burn in the manifold.
On a later-model vehicle fitted with a catalytic converter, the Thermactor system also helps supply the oxygen needed by the catalysts to do their work.
The air comes from an engine-driven air pump, pushing air through rubber hoses to the distribution system for each manifold. In my 1967 Ford Thunderbird, this involves metal pipes, while in later engines this is integral to the intake manifold, to holes drilled through the cylinder head all the way through to the exhaust manifolds.
The system is complicated by two factors. The first is that if the throttle is closed suddenly, the Thermactor system can make the engine backfire; to prevent this, a device called the backfire diverter valve, operated by high manifold vacuum, diverts the air flow to the atmosphere. The second issue is that high exhaust system backpressure could force exhaust gases back through the Thermactor system. This is protected against by a one-way check valve in the system.
By itself, the Thermactor system certainly does improve emissions, but nowhere near any remotely modern standard; it does however provide a good adjunct to a catalytic converter. Ford used the Thermactor system at least through the 1970s and 1980s in this form.
Disadvantages of the Thermactor include power loss from driving the pump, from increased backpressure in the exhaust system, and greatly increased heat in the exhaust manifolds from the combustion taking place there. Also, it means yet more stuff under the hood and getting in the way of the engine. Although it's technically illegal, it's common for owners of presmog vehicles to remove the Thermactor system and replace the components with those from an unequipped car.
Information from my Thunderbird shop manual, assisted by Google searches for applicability to later models. Most of this information is probably general to all AIR systems, but I don't have information on any but the Ford application.