Defaultly, basic information about the recruitment and the advert is being send to Career Page with every advert published there. You can find more information about it in this article.
If you create custom fields while configuring the 'Recruitment data' section you can send them via API to your Career Page to present them there.
To do so, go to Settings > Fields configuration > Recruitment > Recruitment form. Find the field with the value, which should be visible on Career Page. Click on it and you will see this fields settings on the right side:
To make this field visible in the integration:
move the switch 'Field visible via integration' to the right so it turns blue
assign a name in the SID field
SID is a unique name of the field which will be visible via API. In the case above the field will be visible in API as 'Vacancies'. SID should be a string of characters without spaces or special marks.
After selecting one or more fields that should be visible via API remember to save changes in fields configuration by using the blue 'Save' button in the right bottom corner: