Child Budgets are budgets for a selection of Campaigns/Shared Budgets within an Ad Account.
There are a number of ways you can select these specific campaigns from the dropdown:
Use Google Account Budget
This will use the Google Account Budgets (formerly known as budget orders) that exist. You can read more about these here.
Select All Campaigns for Account
As it says, it will dynamically include all Campaigns/Shared Budgets that exist in the Ad Account.
Select Campaigns Budgets - Static
This will provide you a list of all the campaigns within the Ad Account and you can manually select which ones to include.
Select Campaigns Budgets - Dynamic
Rather than manually selecting, you can filter by Campaign/Shared Budget name and it will only include those that match the filter criteria. This will dynamically include and remove campaigns as per this filter.
When creating a Google or Microsoft Ads dynamic budget, you are only able to search against the Campaign name. For Facebook you can search explictly for either
Example: Campaign Name contains 'Brand'.
If you added a new Campaign that contained the name 'Brand', then it would automatically be included in this Budget.