Android Security Model

It is a tough question and you might need to read a chapter for a book to understand the concept.

First of all, you need to know about The Android architecture.
The diagram above and the following extract are taken from a book called "Android Security Internals" by Nikolay Elenkov.

Android’s Security Model

Like the rest of the system, Android’s security model also takes advantage of the security features offered by the Linux kernel. Linux is a multiuser operating system and the kernel can isolate user resources from one another, just as it isolates processes. In a Linux system, one user cannot access another user’s files (unless explicitly granted permission) and each process runs with the identity (user and group ID, usually referred to as UID and GID) of the user that started it, unless the set-user-ID or set-group-ID (SUID and SGID) bits are set on the corresponding executable file.
Android takes advantage of this user isolation, but treats users differently than a traditional Linux system (desktop or server) does. In a traditional system, a UID is given either to a physical user that can log into the system and execute commands via the shell, or to a system service (daemon) that executes in the background (because system daemons are often accessible over the network, running each daemon with a dedicated UID can limit the damage if one is compromised). Android was originally designed for smartphones, and because mobile phones are personal devices, there was no need to register different physical users with the system. The physical user is implicit, and UIDs are used to distinguish applications instead. This forms the basis of Android’s application sandboxing.

In short:
It is a Linux
Apps are users
Permissions are groups

Does the day look brighter now?