Yes it is true, your website title is really important. However, this does not mean you should neglect your web page titles. A common website mistake is that the home page – and every other page on the site has the exact same title.
Imagine reading a novel where the title of the book as well as each chapter heading is exactly the same. Or calling all your children just by their last name.

The most important on-page SEO factor is the page title of each web page. Why? Here are the top three reasons from a search engine optimization perspective:
1. Get indexed
Google and other crawled-based engines can index web pages within your site. The title informs them what the individual site page is about and helps engines properly identify and classify the page information.
2. Get found
Keywords and phrases are used in a search engine query to find specific information. A page title is a key location for keywords that can help you get found in search results. The title tag is also used to determine the ranking of your page in their search engine results pages (SERP). Relevant titles do better.
3. Get traffic
Titles that appear in snippets on SERPs are usually generated from web page titles tags. Descriptive relevant titles often result in higher click through rates by search users than those that just have generic site titles (or an unrelated page title).
Simply creating unique web page titles will improve your search engine visibility. After all, isn’t that why you are on the web in the first place?