JIRA is just an issue tracker. Whatever they're doing to you with it is not its fault. 🙂 You're supposed to use it to document and assign work items (stories, tasks, bugs). What has to be done, progress, duration estimates (in days!), attach whatever extra info is needed (links, files) and use the comments to keep each other in the loop and clear obstacles (blockers, dependencies etc.) It's fairly straightforward when used correctly.
You have to have some way of tracking development. If it weren't JIRA it would be something else – but JIRA is commonly used because it's flexible and can adapt to many ways of doing things and to lots of the aspects of software development.