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A rectenna is a rectifying antenna, an antenna used to convert microwaves into DC power. Being that an antenna refers to any type of device that converts electromagnetic waves into electricity or vice versa, a rectenna is simply a microwave antenna, in contrast to the ubiquitous radio and TV antennas. You've probably seen the word rectenna pop up in discussions of solar power satellites, or other power generation schemes involving microwave power transmission or beaming.
Rectennas are quite good at what they do: efficiencies above 90% are quite common. Inverse rectennas, which convert electricity into microwave beams, are only in the early stages of development, with efficiencies of only about 1%. This poses a problem for solar power satellite proposals.
There has been some research involving microwave power transmission for getting power to communities without wires. One obstacle for such research is the public's view of microwaves as dangerous radiation, through the waves' association with microwave ovens. However, power densities used for proposed microwave power transmission systems are quite low, similar to the leakage from a conventional oven and only slightly more powerful than the radiation generated by a cell phone. Extensive studies on tens of thousands of employees in the electric power industry has shown that they do not experience an elevated incidence of cancer or any other malady through exposure to the waves, contrary to pseudoscientific viewpoints exposited throughout the late 20th century.
A rectenna suitable for receiving energy beamed from solar panels in geocentric orbit would need to be several miles across. Although power densities of such an arrangement would be low enough to avoid any damage to people or the environment, there are some security concerns that energy on such platforms could be focused and used as an energy weapon, similar to the Active Denial System (ADS), a.k.a., "pain beam" employed in Iraq, but on a much grander scale. This problem could possibly be avoided by building the solar satellites in such a way that adjusting the focus by any more than a small margin is mechanically impossible.