Microsoft Flow is a workflow solution that works across Office 365 and beyond. In the Modern SharePoint Online world, Flow replaces SharePoint Designer Workflows (for most things, you can still use SPD Workflows for the moment if you really must).

Flow Approvals allow a user to submit an item for approval and then carry out an action once approved. It includes actionable email notifications and is supported on mobile devices via the Flow App.

This video walks through the out of the box Flow Approval follow and explains how the various steps work. Once you are familiar with Flow, you can easily update and extend this Flow to carry out additional actions or multi-stage approvals.