A mobile payment system is the ability to transfer funds and/or pay or receive money, using your mobile phone.
The mobile phone is simply the medium or to better phrase it, your interface to the payment system.
In most instances, you would either be running an app on your phone, which is then tied to some payment instrument (credit cards, debit cards, banking account, etc.) or you might have a payment service provider who is able to work with your cellular company to provide portable credits, i.e. the credit balance on your phone is able to transfer balance.
In branchless banking, the mobile is the bank. It allows you to do all sorts of payment activities using the mobile phone.