Framework is an overloaded term that can generally refer to some unit of modularized code or a software framework.
iOS Device Frameworks
The iOS SDK consists of dozens of device frameworks. These frameworks are typically suffixed with "Kit" and provide developers with the classes needed to build different aspects of their applications.
UIKit provide the basic classes for all iOS apps.
Here are some common and more specialized frameworks:
Frameworks can also generally refer to "libraries" or modules.
The open-source community thrives with many libraries and modules that all developers can utilize and benefit from quickly. Some popular and commonly used ones are listed here (and this list is by no means exhaustive):
A much more complete list is available at vsouza/awesome-ios.
CocoaPods is the de facto tool used by iOS developers to manage their code dependencies. Most popular frameworks (such as the ones listed above) are available as pods. The CocoaPods tools and ecosystem is very actively maintained and developed.
Open-source Originate Frameworks
We have a private CocoaPods specs repo for our growing list of internally-spawned modules.