Cocoapods is an Objective-C library dependency manager that allows developers to specify dependencies and their versions in a Podfile. It supports private pods through custom spec repositories that can host podspecs for any code, allowing pods to be installed from git repositories, URLs, or local paths. Using many small, decoupled dependencies promotes modular code while avoiding overly broad dependencies. Developers should carefully consider potential dependencies based on metrics like commits, issues, and code quality.