How to check iMessages

See the following from Use Messages in iCloud - Apple Support

You can use Messages in iCloud on your iPhone, iPad, iPod touch, Apple Watch, and Mac. For your privacy, Messages in iCloud is end-to-end encrypted,* which means you can't view or access Messages online via browser. 

You don't 'check' messages in iCloud.. if you are expecting to go to iCloud.com and view your messages, that's not how it works.

Messages in iCloud is used for syncing between Apple devices that share an Apple ID.