Efflorescence is the alkaline components that make up masonry materials. They are being leached out of the masonry and collecting at the surface. Often light deposits can be removed with water and a scrub brush but heavy deposits will need more work.
For interior areas I prefer to use TSP, trisodium phosphate, and a lot of scrubbing. Plain white vinegar and water, mixed 50-50, can also neutralize these deposits. The vinegar can damage delicate materials and change the color of brick, be careful.
For exteriors a pressure washer is the best tool. This alone can remove most deposits.
Commercial masonry cleaners also do a good job on heavy deposits. These are available at your local paint store or home improvement center. A strong TSP solution can also be injected into the water stream if a commercial pressure washer is used. It is most likely that a little scrubbing will be needed.
Both interior and exterior masonry can be treated with the same chemicals. Make sure you rinse the affected areas well. Don't worry if a little effervescent still remains, this will be neutralized and sealed with a good masonry primer like Zinsser 123 or a sealer like Seal Krete Heavy Duty Sealer.