When you add billable items; such as time, travel, products or expense to a matter you can select who has to pay for it. Most of the time this is the "same as client" but sometimes it can be someone different. 

Lets say you are working on a matter where two individuals have a stake and they decided to pay for your work on separately. John will pay for work on everything related to part X of the matter and Dave will pay for everything related to part Y of the matter. This is still the same matter so you want to keep it as such in Manor - the only thing needed is to decide who pays for what. That is where payer feature comes to play.

When you are adding a billable item, such as an time entry, you can see the Payer field.

In this field you can select any of your listed payers. If you need to add a new payer, close the add time modal window, navigate to Clients in the left main menu and add it there. Then you can select it from the list. If your payer is in the list just select him and add the time entry. That's it!

How to invoice a matter with many payers?

That is an easy one. When you decide to create an invoice you navigate to Invoices and click Create invoice button. There you will see all of your matters with an unbilled balance. You can filter by the matter in question and then see to payers listed and both with unbilled items from the same matter. Then you just do your invoices for each payer and your done!