You would be surprised how many people don’t set an offline image on their Twitch channel, considering how easy it is and how well it can sell the brand when done right and on all devices.
How to set up an offline image on your Twitch channel
Once you have the image (image dimensions and file type guide down below) then head on over to your creator dashboard, if you need a reminder – it is here.

Then, find your brand settings. You can find that option here.

Still in this menu, scroll to the bottom to find the Video Player Banner option. This misleading option is where you set your offline image. It does say it in the description “This is displayed on the player when your channel is offline.”.

Interestingly, they call it a video player banner because it is where your videos are at and NOT that you can upload videos as a banner (although gifs are close).
Simply upload your file and you have now set your Twitch offline image! Well done!
Keep reading for more information about this image.
What dimensions should you set an offline image?
For optimal and high quality images, the image should be 1920×1080, this has a 16:9 ratio similar to most widescreen TVs and monitors. The image should be as high res as possible since the 10mb limit is generous.
See more about Twitch image sizes here.
However, mobile phones are not 16:9 (unless they are horizontal) so you should aim for the content within this image to have plenty of buffer on both sides and above and below. Here’s a better way to explain it from CAR.

Aim to have your important content inside the green area in the bottom right image.
Can you have a GIF as an offline image?
Yes, you can have a GIF (graphics interchange format) as an offline image. They do tend to look better (when done well) but are harder to make if you aren’t a an artist yourself. Here’s an example:

What does it look like when you don’t set an offline image on Twitch
Here’s an example of what it will look like without one:
Desktop

Mobile

As you can see, it is low effort and its repetition of the streamer’s user name. If the offline image looks cheap it could make the streamer look cheap.