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Campaign groups are a feature in Google Ads where you can group similar campaigns and put them together in a group. A campaign can be added to only one campaign group at a time. It can’t belong to multiple campaign groups.

In the Shopping Campaign Management tool, when multiple campaigns are created they are created as part of a campaign group. Shopping campaigns that are part of a campaign group are refreshed together and allow the refresher to also create new campaigns when required.

For example, if there are 14 brands in a feed and you choose to create one campaign for each brand, the Shopping Campaign Management tool will create 14 campaigns and put them in one campaign group. When a new brand is added to the feed, the Shopping Campaign Management tool will check the campaign group and when it finds that there is no campaign for the 15th brand, it will create a new one. 

When campaigns are removed from a campaign group that was created by the Shopping Campaign Management tool, they are treated as not being there and the Shopping Campaign Management tool may create a duplicate campaign.

It is recommended not to remove/add the campaigns manually in a campaign group, as this can mess with the campaign group settings, and make the the tool not behave as expected when refreshing the campaign group to resync the campaign with changes in the merchant feed.
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For example, if you create a single campaign in a buildout, the setting is 1 campaign in a campaign group. But if you add another campaign manually to this campaign group, the campaign group setting is to have only one campaign with a given hierarchy, yet now it has 2 campaigns. This might end up making changes that are not expected.
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Another example is when the campaigns are created at the Brand level, and a new campaign is added at the Product Type level, resulting in an inconsistency.
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If there are changes done in the hierarchy, and they do not match with campaign group settings, the system will not be able to make the desired changes.