In SAP B1, Basically when we raise Accounts Payable(A/P) 
Invoice means we are crediting the Vendor and Debit the 
Expenses. And when we are paying to that Particular Vendor 
or General Ledger account,we use Outgoing Payment and 
Select the Payment means through which we are Paying and 
raise the Outgoing Payment.
     Similarly when an Account Recievable(A/R) invoice is 
raised us to the Customer Account and when we receive the 
Amount from that,then we will raise Incoming Payment.

Outgoing Payments need not be only in relation to Account 
Payable Invoices. It can be for any payment to third 
parties be in Vendors or Government dues (Excise Duty). In 
case we create the employees as vendors direct payment of 
Salary(Outgoing) can be created. Outgoing payments also 
arise when we have received advance from customers and we 
need to pay it back to them.

The same applies to Incoming Payment - the only difference 
is that usually Government dues are not received back.