What is Dynamics 365?
Microsoft has merged Dynamics CRM Online with Dynamics AX to form Dynamics 365, a new platform to manage Sales, Service, Project Management, Finances, and many other aspects of your business. Dynamics AX will be renamed to Operations, another Business App available in Dynamics 365.

Currently only the Enterprise edition of Dynamics 365 is available, but coming in Spring 2017 the Business edition will be available, along with new Marketing features.
What is changing?
Dynamics 365 will include the same Sales and Customer Service functionality you're used to in Dynamics CRM, along with PowerApps, Field Service and Project Service Automation. The Operations component shown above is going to be equivalent to Dynamics AX 7 (note Operations is available only for the Enterprise edition, Business edition will have 'Financials', formerly called Project Madeira).

There are also net-new features to get excited about, including:
How will this affect me?
Licensing
The licensing model for Dynamics 365 is changing significantly, focusing around the ability to only license the features that are needed on a per-user basis, allowing for lower costs, and more adoption throughout the organization. The Enterprise edition will include the ability to license individual apps, such as assigning Sales to one user, and Customer Service to another, or subscribing to a Plan, which includes discounted tiered pricing.

Check out Dynamics 365 Licensing Made Simple for more details, and the Pricing Calculator to see how the new license model will affect your business.
Functionality
Look & Feel will remain unchanged for Dynamics 365, with added functionality through PowerApps, and the AX components, which are now called Operations.
Features being deprecated in the near future include:
- Email Router (Server-Side Sync with support for Hybrid scenarios is the current recommended solution)
- Older Mobile OS versions (Including iOS 8, Android 4.3 and earlier)
- CRM List Component for SharePoint
- Office 2010 support
- Legacy Form Rendering
See here for more details.
How can I prepare?
Dynamics CRM Online customers will be automatically upgraded by Microsoft over the next several months. Getting familiar with the new licensing model, features, and functionality will help ensure that when your organization is upgraded your users are excited and prepared.
Dynamics CRM On Premise customers with Dynamics CRM 2016 can upgrade directly to Dynamics 365. If you’re on an earlier version than 2016, you'll have to upgrade to the next most recent version until you're on 2016, and then you can upgrade to Dynamics 365. You Microsoft Partner can assist with upgrading your environment, and the new Dynamics Lifecycle Service is a great way to ensure the process of moving from an earlier version of Dynamics to Dynamics 365 is quick and painless.