Search engines actively spider web sites seeking for indicators on what the site is about. These spiders go from page to page and feed the content back to algorithms that help determine meaning and value. A significant key to helping search engine spiders figure out what your pages and site is about is to tell them. They value certain elements of a web page more than others. Web page titles are very valuable.
A page title is found in meta tags in the HTML of a page. They are also displayed in your browser header. Look at the top of the browser or in the current browser tab and you'll see "Composing Great Web Page Titles". The browser pulled that title from our HTML. Search engines do the same thing. When they hit a page they search out the title tag and display it in the browser.
Title tags are essential in solid SEO practice.