Before I start please note jailbreaking (an Apple Device Term) and Rooting (an older term ported over to Android and other devices) both have the same meaning:
It is the process of removing limitations on the device’s operating system through the use of software and hardware exploits.
There are many Reasons for Jailbreaking / Rooting but the most pointed out reason is to expand the feature set limited by the manufactures.
Apple (being one of the manufactures) checks apps for compliance with its iOS Developer Program License Agreement before accepting them for distribution in the App Store. However, their reasons for banning apps are not limited to safety and security and may be construed as arbitrary and capricious. In the case of Apple to get access to the list of banned apps, users rely on jailbreaking to circumvent Apple’s censorship of content and features. Jailbreaking permits the downloading of programs not approved by Apple, such as customization apps used to change the User Interface.
Note here that many of the changes to the User Interface in early Jailbroken apple devices have been implemented in the newer operating systems like iOS 7+.
Again with Apple, since software programs available through Cydia (a Jailbroken app) are not required to adhere to App Store guidelines, many of them are not typical self-contained apps but instead are extensions and customizations for iOS and other apps. Users install these programs for purposes including personalization and customization of the interface, adding desired features and fixing annoyances, and making development work on the device easier by providing access to the filesystem and command-line tools.
By Jailbreaking / rooting your device you run the risk of lowering Security, privacy, and stability. Again using Apple as an example, Apple claims to keep Security, privacy, and stability at an all time high. Every so often mistakes happen and Security, privacy, and stability are lost due to poor coding and lack of watching the code. Apple (being good to their name) do upgrade fixes as soon as Possible when there is a fix. Using Android as an example, fixes come from Google as quick as they can but get filtered by the many manufactures using Google Devices to add their own updates and software patches. On some Google Devices many months can go by before the fix is upgraded to the devices in question. In some cases I have noted the delay in years… Not great for Google Devices…
One thing to concern yourself is the legalities of Jailbreaking / rooting your device. In many countries it is justified (by law) that the manufacture can not only void your warranty of the device in question but may also submit you with copyright and infringement laws with legalities attached to it. I for one limit the need in such cases… Void the Warranty but if I purchased the device and paid full price for it then I can do anything I want to it for my own needs, as long as I don’t sell it to make money after modifying it. Then manufacture programmers might even get a leg up on this and further their careers with this solution…
You should also watch out for exploits and Viruses. There are many programmers just waiting for the next victim to jailbreak / root their device and not read all the documentation relating to the conversion. Exploits in the past have been a SSH (secure Shell Command Line) was installed by default with a default password that was never changed. The hackers know this and use this to take advantage of the new hacked device to use for their own needs. Some cases user names and passwords were stolen along with email address. Other information were bank details and online financials. It even heard of ghost devices being setup. Just like ghost computers where hackers use the computers as their own hacked network to do illegal activities without getting caught. We know the new smart devices are really small powerful portable computers that when converted to ghost status they change to portable powerful ghost computers that are harder to track down and thus more appealing to the hackers at large.
Do I jailbreak / Root my devices…. Not yet… The the thought of adding more control to my portable devices that the manufactures restrict and have always been there seems more and more appealing… My self being a very good programmer does not like the idea of the manufactures saying what apps I cannot install on my bought device. There are a lot of ideas I wish were on my device that are not designed (let alone programmed and approved) yet and I think I can do them myself… So soon I will be Jailbreaking / Rooting my devices (for my own needs) and tell the manufactures where to go.