First I must make sure you know exactly what a pdf (Adobe) file is.  PDF files are made up of individual pages.  Each page is a separate image much like a photograph.  Just as a photograph any words within the image (individual page) is not recognized by the computer as text but as an image.  It may appear to you as a file within a word processor file but the two are totally different.  As a standard pdf file the individual pages cannot be searched because the text on the page cannot be recognized in it's raw form. 
    When a pdf file is rendered searchable it is run through a program which analyzes each page and interprets the image looking for text.  It then recognized the letters as words and forms a second lawyer under each page containing the words it has recognized by examining the page image.  It is that layer that is then searched.  Obviously the search will only be as successful as the conversion.  In other words if the program that examined the individual pages was not able to recognize the letters within a word it could not convert that word into a search result.  Besides the possibility of conversion recognition error the other potential problem is the resulting file will be larger.  This really does not effect you as a user but as a programer it can sometimes limit the amount of files I can put on a CD - I can place many more unindexed files on a CD then indexed.
    Once a file is indexed the search process is easy.  It works very much like a web search.  After opening the file in Adobe Reader click on the search option in the menu bar at the top.  A search box will open.  Write in any word you wish to find and hit search.  A result list will appear as soon as the pages are scanned with the word you searched highlighted and linked to the resulting pages.  This option is extremely helpful as it means you can search an entire text in minutes without actually having to read the complete text.  However, it should be used as a first process and then a closer examination of the text is recommended.  The reason for that is the accuracy rate of the indexing is still under 100%.  I hope this makes it a little clearer.

Good luck in your research and if you have any other questions please feel free to use the email link on this page.   NOTE to those more experience reading this explanation - this explanation is written simply in order to help explain a difficult process for some to understand.  It is not meant to be technically interpreted!!