This system also goes by the name 'onsite payment,' and it allows you to handle transactions on your site. However, the final process gets dealt with by a payment gateway service provider. It works by displaying the forms on your site while the provider works on data collection, submission of information as well as responding to users.
The user, however, will not be aware of the service provider and this gives you an avenue to customize the receipt page.
You are in a position to maintain data sensitive to your customers, and you can use the system as an opportunity to work on your branding.
With this mode, PCI compliance is a must. In a case where you lack one, you can make do with an SSL certificate. You also have to work at improving your security as you will be handling sensitive information.