Action Details
Requirements and how-to articles for Twitch's action:

A VOD (Video on Demand) is past streamed content on Twitch.

You need this to get it done:

Enable VOD Saving
You need to tick the checkbox next to "Store Past Broadcasts" in your Dashboard settings (it is disabled by default.)
Managing your Videos
Once you have enabled VOD saving, Twitch will automatically save your broadcasts. They are kept 14 days for non-turbo users and 60 days for Twitch Partners and Twitch Turbo users.
Highlights allow you to curate your past broadcasts into shorter video segments. To highlight a specific part in a VOD you can do so by using the Video Producer. Unlike full broadcasts, highlights are saved permanently (unless you delete them.)
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How-To Articles
A list of useful links for you:

Twitch Customer Support - Videos on Demand
Information on enabling and managing VODs.
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