To optimize your Twitter shares, you can customize your Twitter Template and setup Twitter Cards.
With Twitter Cards, you can attach rich photos, videos and media experience to Tweets that will drive traffic back to your website. By simply adding a few lines of HTML to your webpage, users who Tweet links to your content will have a "Card" added to the Tweet that’s visible to all of their followers.
How to Setup
Some CMS' like WordPress and Drupal have SEO and Metatag plugins available that make the job of adding pertinent meta tags to your pages 1-click easy. For WordPress, WordPress SEO by Yoast or All in One SEO Pack plugin are great options. For Drupal 7 and 8, the Metatag module is a popular option.
How to Verify
Once you've added the pertinent meta tags to your page either via a plugin or directly in your template, run your URL against the validator tool to test and preview - https://cards-dev.twitter.com/validator