Turn it on under Settings > Mail Settings > Event Webhook (or the equivalent API endpoint) and pick which event types you want posted: processed, delivered, open, click, bounce, dropped, deferred, spam report, unsubscribe, and group unsubscribe/resubscribe for sends using subscription tracking. Each event arrives as a JSON object carrying the recipient address, your own custom message metadata if you set any, a timestamp, and event-specific fields, a bounce reason and type for bounces, the clicked URL for a click.
SendGrid batches events and can send more than one per request, so the endpoint you build needs to parse an array, not assume one event per POST. SendGrid also signs the payload if you enable signed event verification, which your endpoint should check before trusting the contents, since the URL is otherwise a public endpoint anyone could post to.
Inbound Parse is a separate setup: you point an MX record at SendGrid, and incoming mail to that domain gets parsed and posted to your webhook as structured fields (from, to, subject, body, attachments) instead of landing in an inbox. It's the feature behind things like a support address that turns a reply into a ticket automatically, or a reply-to address that updates a record instead of going nowhere.