Back to the matter at hand simply means to return to the topic of conversation that was being discussed prior to whatever interruption occurred. It is a phrase that can be used in any number of different contexts, whether in a professional setting or even among friends.
When used in a professional setting, back to the matter at hand could mean to put aside personal feelings and focus on the task at hand. This phrase can also be used to refer to a group returning to the point of discussion that was interrupted, such as a meeting in a corporate setting.
In more casual contexts, the phrase back to the matter at hand can simply be a phrase used when returning to talking about the topic being discussed before being interrupted. In addition, it could be used when the conversation has moved off track and the speaker wants to return to what the conversation was initially about.
Regardless of the context in which the phrase is being used, it is a simple phrase that is used to help people return to their previous conversation.
