There isn’t any way to download Cydia without jailbreaking. Lots of people ask Cydia without jailbreaking. They think, they will lost App store apps after the jailbreak. It is wrong. By jailbreaking you can get Cydia app as well as App store apps. And also, there is no way to download Cydia without jailbreaking.
You must jailbreak your device if you want the Cydia.
Apple doesn’t allow to install any third party applications to their products. Apple has locked the system root of all iDevices. Cydia is the most popular third party application for Apple devices. When you jailbreak your device using a compatible jailbreaking tool, it installs Cydia automatically to your device.
When you install the Cydia you can download thousands of liberated apps, themes through Cydia’s apps manager. You can use Cydia to manage third party liberated apps. It act as the Apple app store for liberated apps. But many of Cydia apps are completely free to use. You can install awesome system and general apps for free through Cydia. Cydia apps are not available in Apple App Store.
Conclusion – You must have Cydia if you want to feel real experience with your iDevice.
If you have already jailbroken your device and Cydia has been disappeared accidentally you can use iFile to restore Cydia.