A Package Manager is the backbone of software distribution. It handles dependency resolution, versioning, and installation paths. For your custom OS environment, you can architect a lightweight manager using simple shell logic and tar archives.
A remote repository is essentially a web server hosting compressed binaries and a metadata file (index) that lists all available packages and their checksums (MD5/SHA256).
You can simulate a package manager in Termux by creating a script that pulls binaries from your own GitHub repository or local server.
Advanced architects implement a "Dependency Tree." If Package A requires Library B, the manager must automatically detect and install Library B first to avoid Linking Errors.