Command
pm-releasenotes (alias: rln)

Syntax
drush rln [project]

Example
drush rln colorbox

I went ahead and installed and enabled version 7.x-2.0 of the Colorbox module (I also installed the Libraries module as it's a dependency of Colorbox). Its current latest version is actually 2.4, so let's take a look at the release notes to see if there is anything that we need to pay particular attention to before we update.

(Note: When you type this command, you are taken into the VI editor. You can use the up and down arrows to move around. Or, the "D" key to move down a half page at a time, and the "U" key to move up a half page at a time.)

When we type the command, we can see the full release notes for all versions of the Colorbox module. You'll notice notes for the 1.x version as well as the 2.x version. Right off the bat, you'll see that the 2.0 version requires the 2.x version of the Libraries module. So, if we were upgrading from Colorbox 1.x to 2.x we would have to make sure to also update the Libraries module from 1.x to 2.x. I'm already running the 2.0 version, so I have also installed the 2.x version of the Libraries module.

If we scroll down, we'll see that the 2.1 release of Colorbox may require an update of the Colorbox library as well. Let's check which version I have installed.

We'll go to "sites/all/libraries/colorbox" and open up the file "README.md" with a text editor. In this file we see that our current version is 1.3.21, and we need at least 1.3.21.1. So, I will need to update the library in order to use the most recent version of the module.

If we keep scrolling down, we can check to see if there are any other manual updates that we will need to perform. When we get to the bottom, and view the release notes for the 2.4 version of the Module, you'll see that it still states that we need to update to at least the 1.3.21.1 release of the library. Something to keep in mind is that while this particular module specifies the library requirement with each release, some might only mention it in the first update, and then, with the next release, assume you've already updated the library, and not mention it again. So, if you're skipping one or more updates, as we are here, it's important that you read the release notes of each release between the one you have installed, and the one you're installing, to make sure you perform any manual updates that may be necessary.

When you're done reading the release notes, just push the "q" key to quit the VI editor.

The way you can check release notes outside of Drush is to go to the module page for each module you are updating, scroll to the bottom and click "View all releases". Then you can select your version of Drupal and click "Apply" to filter out the rest.