For Simple Invoices to be able to send email you need access to an smtp server. This can be your ISP's smtp server or other. But if you don't have access to an smtp server you can install one on your PC. Below details some of the available option for each operating system
If your not on mac osx server or sendmail isn't installed on your system you can use the below listed:
If your version of linux doesn't already come installed with one of the below listed mail servers, please install one as per your distributions installation procedure
If you have already setup smtp on your system please feel free to post in the discussion section below details on what you used and how you did it.
You can use Google GMail to send emails in Simple Invoices - refer: