This is part of the "non-synchronization" stack that is available for JIRA 4.3 and higher. This allows you to create "Custom Fields" which are used to associate a JIRA issue with any Salesforce.com object. This can either be a 1 to 1 (using the Remote Object Link custom field) or a 1 to many configuration (using the Multi Remote Object Link custom field).
Using this method, you are still able to see the various attributes of the Salesforce.com object (configurable to display various fields of the object), however you will not be able to update the fields of the linked Salesforce.com object from within JIRA (you will have to log into Salesforce.com to do this). In a way, it is only a read-only method from JIRA.
Uses less API calls (as it does not need to update the Salesforce.com object, only retrieve information from it).
Allows 1 to 1 or 1 to many Salesforce.com object links.
Can link a JIRA issue with multiple Salesforce.com object types.
The data will not be available in JIRA when Salesforce.com is unavailable (e.g., for scheduled maintenance).
The information can only be updated in the respective system (e.g., you can only update the Case from within Salesforce.com and can only update the issue from within JIRA).
When Should I Use This?
You should use this if you would like to link many Salesforce.com records to a single JIRA issue where the user in JIRA does not need to update the Salesforce.com object (and vice versa, the Salesforce.com user does not need to update the JIRA issue).
For example, you could use Remote Object Link to associate several Salesforce Account records to one JIRA issue.