It is said that applications in smartphone operating systems work inside a secure sandbox. What sort of security does it provide?
If it is secured, and other applications do not have read write permissions to another app, then how does inter process communication come in to the picture? If processes(applications) can communicate via interprocess communication methods, how does it bypass the sandbox?
Your question is very broad, but since it is tagged with blackberry-10 I assume you are interested in this platform specifically.
At the lowest level, the QNX kernel is essentially an interprocess communications system. The kernel doesn't actually do anything other than pass messages from one process to another. So that is how IPC is managed at the low level.
At the highest level, and most mundane implementation, BB10 uses shared files. If the owner grants an application permission, it may read from and write to a set of directories that are shared with other applications given that permission.
For direct IPC BB10 has what BlackBerry calls the invokation framework. This allows processes to share not only data, but executable code and user interface elements. The owner sees this as the saring system, and cards.