The short answer is: yes, optimizing your images is an important thing to do because it improves your website's rank and performance. Google has an article confirming the importance of page speed here.
There's also a tab within Google's Webmaster Tool that will show you how fast your website is as it's experienced by people around the world.
what is an optimized image?
An optimized image is an image designed for one of the three mediums we surf the web on: desktops, tablets, and mobile phones. Of the three, SEO experts are most concerned with the mobile version.
There are a few reasons for this. First, large images (images sized for desktop) load slowly on mobile phones. Second, they consume more bandwidth than necessary.
But the slow load does more than negatively affect your website's organic rank. It increases the chance that the person viewing your site on their phone won't wait around long enough for all the elements to load.
In other words, they'll leave your site before they read your site.