The <title></title> tags reside within the <head></head> tags. The contents of the HTML title tag shows up in two different places.
First, you find the title information at the top of the browser screen (above all the task bars). The second place your find title information is at the top of the definition in most Search Engine results. The rest of the world is told this is the title of your web page.
Many search engines limit this field to 60 characters. Make sure you get the important stuff written into the HTML title tag first.