Your customers will navigate on your website and your URL to add the products and services they wish to purchase. You, the merchant, will render a SSL check out page where the payment information will be entered by the card holder in their browser. Again, this is on your website and your URL. Once the cardholder clicks "submit", all the payment information is posted behind the scenes to Braintree. We'll pass back the approval or decline information so you can show your customer the appropriate page.
The experience is entirely transparent to the cardholder. This way, you don't have to use a hosted page and compromise the flow, structure or handling of your checkout process.