Office 365 is a cloud service from Microsoft.
Part of the service it provides is cloud-based version (Microsoft hosted platform) of SharePoint 2010. The benefit you get is that you don't have to worry about setting up and maintaining the SharePoint 2010 environment/infrastructure yourself.
Depending on which plan you get, you are able to leverage SharePoint 2010 in addition to other Microsoft tools such as Exchange, Office and Lync.
To get maximum options and for your SharePoint solutions to function correctly it is recommended to get an Enterprise level plan (either E3 or E4).

Try out the cool/new/free way to get your hands on experience of SharePoint 2010.
More Development related posts to follow.