Think of your hard drive like a dictionary. Without an 'index', your computer is just going to look for your file 'alphabetically' (not really, of course, its just a metaphor). In particular, it doesn't know right away where, say, files starting with 'D' are stored. So, without an index, the hard drive has to be searched a bit.
Now, think of an index as little tabs on the pages for each letter -- so a search can skip straight to D, or E, or whatever letter you like. Now a real index is quite a bit more complicated than that (i.e. there have been hundreds or maybe thousands of PhDs in database systems studying indexing), but you should get the picture.
The only trick is: Unlike a dictionary, sometimes the contents of your drive change. That makes the index stale, and it occasionally has to be re-built, which can take awhile.
Edit: Typo