When the form is submitted, some PHP code sanitizes the provided data, then saves it in the user meta table. Each field might only be a line or two of code. Once the data is in the user meta table, any other code for other pages can access this data and do things with it. At the very least, form fields can be pre-populated with this data so users never need to reenter data unless it needs to be changed.
The data can also be used to compile statistics, like the number of users from various countries for example.
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