The mobile emitter is a small device from the 29th century that lets a hologram leave holodecks and sickbays and move about freely.
Voyager's Doctor obtained the emitter in 1996 Earth, where the industrialist Henry Starling had been exploiting 29th-century technology recovered from a crashed timeship. Starling downloaded the Doctor's program into the device, and after the crisis the Doctor kept it, freed from the limits of fixed holographic projectors.
The emitter allowed the Doctor to join away missions and explore planets in person. Because nothing comparable existed in the 24th century, its loss or damage was a constant concern for the crew.