An autoresponder is a computer program that generates a response to an email, request, or action. Autoresponders were initially used to notify a sender of an undeliverable email, but now they are often used in email marketing. Autoresponders can give you the ability to send a customer a pre-written email when a specified event takes place, such as a customer creating an account or purchasing a product.
Autoresponders can be outsourced to an Application Service Provider that provides the infrastructure and support for the autoresponder.
Autoresponders can also be installed server-side, giving you complete control while requiring you to provide the infrastructure and technical skill to maintain the autoresponder.
You can set up an autoresponder with SendGrid, by utilizing the Inbound Parse Webhook and the v3 Mail Send endpoint.
More information about autoresponders can be found here.