References can only be published if the particular entry has at least one linked reference. You can choose to publish every reference, or just a certain group.
To publish all references:
Navigate to the references tab on any entry and then click Publish all.
To publish only a group of references:
Select only the references you wish to include, and then click Publish selected.
Contentful will check if there are any errors on particular entries or assets. If so, nothing else will be published, avoiding any inconsistencies with your content.