A rotary converter (also called a 'synchronous converter' as it runs 'in sync' with its AC power side) is a large electromechanical device that performs the same task as a
rectifier - that is, it converts high-voltage
AC power to
DC power. They date from the late 19th to mid 20th century, when solid state rectifiers either hadn't been invented or were as yet unable to handle the industrial power loads that rotary converters could.
These devices were built mostly to support electric railroads and large industrial systems. Electric motors ran on DC current because AC motors could (at the time) only run at speeds which were fixed multiples of the input power frequency and hence it was not possible to alter their speed. In the case of railroads, they spent most of their time a great distance from the generating plant - which meant that AC current was required to transport the power from the generator to the nearest breaker point on the railway system, as until recently only AC current could be transformed between voltages, and hence be transmitted at the extremely high voltages required to minimize losses. As an example, the New York subway was originally built with a single large generating station which produced 11 kilovolts at 25 hertz AC. This was sent to the various substations on the system, which used transformers and rotary converters to turn it into 600-volt DC power. This latter is what was fed to the 'third rail' for the trains.
A rotary converter functions sort of like a hybrid of an electric motor and a generator. It's perhaps easiest to think of it as a generator which is turned not by a mechanical power source like water or steam turbines, but by the incoming AC or DC power source. If you are familiar with electrical engineering, you can think of a rotary converter as a synchronous AC motor, with slip rings on the armature to cause it to turn, and commutator brushes positioned to capture DC power from the turning armature. It of course could also accept DC through the commutator as motive power, and in that case would output AC from the slip rings.
It would be possible, of course, to simply pair the output shaft of an AC motor with the input of a DC generator and get the same result; however, the rotary converter contains many fewer aggregate moving parts, and hence suffers from fewer losses to friction and induced heating from the magnetic field. Plus, unlike the pair, it is much more easily reversible.
Rotary converters need to be 'started' in order to function - that is, they need to be spun up to the proper speed to 'synchronize' with their AC input. They can be spun up either mechanically, by applying force to the armature to spin it; or by feeding power in from the AC side (with additional 'starter' windings to properly spin at low speeds) or from the DC side. In the New York subway, they were generally either spun up via auxiliary motors or, once the first converter in a substation was running, by back-feeding DC from that converter's output to the others to bring them to speed.
As a consequence of their being mechanical devices, they suffered from wear and the possibility of breakdown. Starting and stopping them was difficult enough that it required personnel to be available to do so - in New York, there were teams assigned to spin converters up and down to match the demand changes which resulted from commuting patterns (rush hour, etc.).
Eventually, a device was invented called a mercury arc rectifier which could handle the enormous power loads that the rotary converter was used for but with no moving parts, and some time after that solid-state rectifiers were built which could accept the megawatts. Nearly all rotary converters in the NY transit system have been retired. Several are in museums, and others sit and rust quietly in the powerhouses which now run solid-state - being far too heavy to bother removing. This doesn't mean that the device is gone, however; smaller versions are still used today to change the phase of AC power at the consumer end relatively cheaply - say from two pole, single-phase to 3-phase AC(thanks to rootbeer277 for correcting my rubbish parroting), rather than from AC to DC.
(A page with Images of NY Subway rotary converters)
Sources:
Iron Noder 2010