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"