The quick answer is "Search Results" is the number of results
(web pages found) and return for a certain search keyword.
For example "dog houses" yields 8,100,000 google search results for that keyword search.
As for search requests - It is the number of times a keyword or phrase is search for... such as the number of times dog houses is searched for
(at a search engine) daily or monthly which is 830.0 /day.
here is a tool to find your own search requests.
http://www.digitalpoint.com/tools/suggestion/?keywords=yahoo
The idea obviously is to create your pages around these high search requests because they will yield the highest possible visitors to your site.
Stay away from the keywords that dont bring in any search requests.
Some would argue with me but I always say that "Search Results" are not really that important.
Sometimes they can be an indicator of competitiveness - but usually not.
Just look at the "search requests" off the page I gave you and if it is high know that there is going to be some competition for it.