a (very
complex; much more complex than I am capable of describing here, especially since
I don't understand it fully, myself) method for
indexing and subsequently
searching documents based on their meaning, rather than on the words that they contain. That takes care of the hence "
semantic" and "indexing".
The "latent" part is the really clever one; instead of actually trying to "understand" a document, statistical information about the structure of its sentences and words is built up, and from that, a it is assigned a point in some N-dimensional space. To conduct a search, the search phrase is analyzed and assigned a point in the same way, and documents are returned based on "nearness" in space.
for more information, try searching google; there is a lot of information (mostly from university researchers). But if you are too lazy to do that, suffice it to say, "it's magic"