An embedded checkout is a way of integrating online payments in which the payment fields are displayed within the merchant's website or app, although they are served by the payment provider. The customer stays on the merchant's page throughout. Technically, the provider's fields load in frames or components through its software development kit, and card details pass straight from the customer's device to the provider.
The approach sits between two alternatives. In a hosted checkout the customer is redirected to a payment page on the provider's domain, which is simplest for the merchant but interrupts the visit. In a fully direct integration the merchant collects card data itself and takes on the full burden of the PCI DSS. An embedded checkout keeps the merchant's branding and flow while leaving sensitive data with the provider, so the compliance scope is small, though the merchant remains responsible for the security of the surrounding page and its scripts.