A normal pulsar has a period of a few tenths of a second to a few seconds. The general physics controlling pulsars suggest that they should slow down over time to longer periods.
Millisecond pulsars have a period of about 1/1000th of a second, and are spinning much faster than normal pulsars. Theory cannot explain the formation of such a rapid pulsar through normal means. The best explanation is that mass transferred to the surface of the pulsar has increased its angular momentum, and rotation rate.
These pulsars are found in binary systems that have a small radius, indicating that they are very old. In order to speed up the pulsars to such high speeds, they must have absorbed a large amount of mass. The companions of these binary millisecond pulsars are very small, in the red dwarf or brown dwarf range.
The conclusion is that the millisecond pulsar has absorbed almost all of the mass of a main sequence star, leaving behind a very small remnant companion which may eventually be evaporated.