The purpose of flagging expenses as reimbursable is to allow you to cut checks for your employees, clients or vendors in Core.
When you mark the employee expenses as reimbursable, they show up in the Bill Payments screen as a payable. This is handy especially if you run checks out of Core. When you create a new check for an employee, it tells you if there are reimbursable expenses associated and allows you to run a check for them.
Even though you can use the same concept for vendor expenses, our recommendation for them is to create vendor bills instead. For vendor expenses that are related to projects, you can use the Items tab on the Vendor bills screen. You can write checks and print them the same way.