The QuickSight elastic network interface is a logical networking component in a VPC that represents a virtual network card. QuickSight creates at least two of these network interfaces to use with a VPC connection based off of the subnets that are attached to it. Then you add the VPC connection to each QuickSight data source you create. The QuickSight network interface alone doesn't give QuickSight direct access to your databases. The VPC connection works only for the QuickSight data sources that are configured to use it.
When you use the QuickSight data source to query a database or other instance within your VPC, all the network traffic from QuickSight originates from this QuickSight network interface. Because the QuickSight network interface exists inside your VPC, traffic originating from it can reach destinations within your VPC by using their private IP addresses. Each QuickSight network interface gets its own private IP address that comes from the subnet you configure. The private IP address is unique for each AWS account, unlike the public IP range.
