There are several ways to integrate Jira data with a third party Business Intelligence system.
One would be via some ETL tool (Extraction, Transformation & Loading). We recommend the SQL for Jira Driver for that as is allows to perform SQ+JQL queries remotely via standard JDBC over the HTTP protocol and in a secure and Jira permissions-compatible way. This method requires some synchronization process to keep data up to date.
As alternative, the XML/A protocol is an industry-standard that allows to connect two BI applications in client/server scenario. The app transforms Jira into a full featured BI server with full support for the XML/A protocol so you might want to to use the your favorite XML/A client tool to explore data. In fact this app deploys the award winning Saiku Analytics Community Edition web tool packed as Jira app and uses it as BI client to connect to the BI Server (Mondrian).
We will use Excel as BI client example to connect to Jira via the XML/A protocol.