So I wrote an really long answer, but Atlassian answers decided to be an annoying tool here it is again:
Bamboo is used to build, test and deploy your software. It works quite the same as travis, teamcity or Jenkins. It has multiple security features and let's you integrate to Bitbucket and JIRA easily. This helps when your working with large projects or want to continuously deploy. Bamboo is called Continuos integration tool and it's pretty easy to use if you know how to build on a command line etc.
Bitbucket is an version control server for git and Mercurial. Its used to control your repositories and keep your code safe. It helps your developers to communicate with each other and develop code together with almost no mess at all. Other similar products are Deveo and Github.
Fisheye enables you to do smart commits that trigger different things for example in JIRA you can move/comment a ticket while commiting your code to bitbucket. This enables faster development for the developer and less overhead to him.
Crucible: Code Review tool it lets your developers talk about quality and how to solve different things easily and meaningfully. It also helps when you are guiding a junior programmer on his way or want to talk about coding standards etc.
Sourcetree is an git and Mercurial client that an developer or manager can use instead of command line tool. It makes it easier to use the version control and work with Github/Bitbucket or Deveo
Bamboo: Continuos integration software such as Jenkins or Travis
Bitbucket: Github/Deveo, etc. Version Control softwares
Fisheye: Smart commits
Sourcetree: git and mercurial graphical user interface
You can also ask for an Atlassian Expert company to come and explain to you how these tools work etc.
Bamboo is a Continuous Integration tool like Jenkins. You would like this to your Git (BitBucket) or Source Code and to JIRA for releases/Builds.
Bitbucket is a Git ,or in the case of BItBucket Cloud, and Mercurial Source Code management application. It would be akin to Perforce or Github and similar apps.
Crucible is used for Code Review and you pair that with Fisheye for browsing/reporting on your Source.
Sourcetree is Atlassian's free Git/Mercurial GUI Client. You would use this to connect to your repositories and pull/push/cone/etc code.
I hope that helps some, i can expand on these if you need as well.
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