While googling various keywords, i found that few websites are showing the exact keywords as a title that we are searching for, but when we open that site found the title is different. I tried to find out the reason but didn’t got anything. 
Can anyone tell from where the search engines fetch that data.
Yes, Many time i’v also faced such type of problems. But, now Google now start spamming such type of the websites. Which is not show the exact result which user want to search.
Sometimes it happens when a page has changed its <title>, and the new title is less relevant to your query than the old one. Google may have updated its index for some queries but not others, and if the old <title> fits better then it might not get round to updating it for a while.
I had visited many sites, and found the title that search engine fetch is totally differ from the original meta title. Regularly notice the targeted site and the site can’t make any changes in the title.
Still confused from where it will take data and display us.
Google has stated that they reserve the right to change the page/meta title if they believe a different title is more useful to users. This could be what is happening, particularly if the text they are showing is contained somewhere else within the content on the page.
Cutts says Google wants to show the titles that it thinks are most useful. “For example, suppose the title of your page is ‘Untitled’ or if there is no title. If that’s the case, we try to show a relevant, useful title.”
“We reserve the right to try to figure out what’s a better title, what’s a more descriptive title or snippet to show the users,”
http://www.webpronews.com/google-may-change-your-page-titles-2009-12
This error occurs due to spam indexing of web pages from webmasters. Google spam these pages and also banned.
if you change the info then it will take a few weeks for it to change and maybe a month. If it is correct on your website then it will eventually show up correctly on the search engine.