Visit the GitHub and sign in, creating a new account first if necessary. Select the specific repositories you would like to watch.

When you watch a repository, you get notifications for any new pull requests and issues that are created, including those not mentioning you.

For example Monero source code can be found in this repository. Monero GUI and Kovri code each have their own repo. You can control what type of notifications you would like to receive and how you receive them.

As a non developer, doing the above will make more sense if you read the GitHub discussions of Monero contributors about recent pull requests. Important and complicated pull requests generally receive multiple comments before being merged. Based on developer feedback pull requests can be canceled or modified or merged to master. If you are not willing to compile from source then following this activity is the best you can do to stay up to date on code changes between tagged releases.