The Licensing How To series posts are provided by our Customer Service Presales and Licensing team members.  These scenario based licensing topics are written on trending topics and issues based on their interactions with customers, Partners and field sellers.  For more posts from the Licensing How To series, search the “Licensing How To” tag on this blog.
A frequently asked Office 365 licensing question that we address on our Team is: what happens if I buy Office 365 but continue to run on premises workloads for certain products? We’ve seen Office 365 Community Forums and other sites light up with something called “dual use rights,” “on premises use rights,” or “on premises access rights.” What does this mean, and how does it apply to me?  Well, the short answer is, it depends.  The basic licensing concept is if you’ve purchased a User Subscription License (User SL, or USL) for an Office 365 Service, that user is licensed to access the equivalent workload(s) running on premises.  While the applicable application server CALs are not included in the Office 365 User  subscription License, a CAL equivalency use right is included to access the on premises application server. 
At a high level, it works like this: Users licensed for applicable/eligible Office 365 services have use rights equivalent to a CAL for the purpose of accessing equivalent on premises workloads.  For example, a user licensed for Exchange Online Plan 2 can use their USL to access Standard and Enterprise CAL features of an on premises Exchange Server.  Below is a table with the three Office 365 services which have “on premises access rights.”  On the left and center columns we listed the on premises product and CAL type.  On the right column, we note the Office 365 User SL with rights equivalent to the on premises product and functionality.

Source: Dual use rights Office365 | Software Asset Management