Recent issue of Axandra Search Engine Facts nicely explains what is semantic indexing and why it is important to you. As it says,

Semantic indexing means that search engines try to associate certain terms with concepts when indexing web pages. For example, Paris and Hilton are associated with a woman instead of a city and a hotel, Tiger and Woods are associated with golf.

Google has billions of web pages in its index. If Google finds that many web pages contain both the word Paris and the word Hilton then Google might assume that these keywords are related. The other words on these pages could give Google a hint that this special word combination is about a woman.