I am not sure that your question is going to be answered in the way you want.
Jira (and most other web-applications) are far more complicated structurally than you can accurately describe bits of them as "front end" and "back end". Where do you draw the line between front and back?
Most Jira users use it in a browser, and the rest use client applications that are built to understand Jira without a browser (that even goes down to the simple REST calls you can make - curl is still a client). The rest of Jira runs on a server. So does "back end" include the database (one of five that work off the shelf? Are you interested in the others that might work?) The application server? The application loaded into the application server? The operating system supporting the read/write of all the files that the system will create, edit and destroy?
On the code level - which "languages" are you looking for? The bits of Jira written in Java, HTML, Velocity, JSP, Javascript, Groovy, Scala, and and and?
I am not saying you have asked a "bad" question. Only that the question is probably too simple and hence cannot really be answered in a way that would be useful to you.
Could we ask for what you're really trying to get at? Why are you asking this question?
(But have a look at the docs Rilwan pointed you to first - they might answer your real question directly!)
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