Adobe Flash Player is required in order to play on Replay Poker as the tables currently run on Adobe Flash. Installing and updating Adobe Flash Player are both very simple as they're done from the same place. To do either one, just visit the official download page at Adobe's website, and click the 'Install Now' button.
It is important to note that if you are using Google Chrome, Adobe Flash Player is built into the browser, so as long as you keep Chrome up-to-date you'll have the latest version of Adobe Flash Player automatically. If you aren't sure if you're up-to-date, just click the menu icon at the top of Chrome, click 'About Google Chrome', and you will be told if you are up-to-date or if you should update to the latest version.
After the download is complete you may want to restart your computer (or at the very least close out of and reopen your web browser) to ensure the installation finalizes.