What is effect of CTRL + Z on a unix\Linux application

A "background job" is just one that is not interacting with the user -- it doesn't control the tty and it just does its thing (generally silently). A foreground job is the reverse, it holds control of the tty to interact with the user.

Control-Z suspends the most recent foreground process (the last process to interact with the tty) (unless that process takes steps to ignore suspension, like shells normally do). This will generally bring you back to your shell, from which you can generally enter the command bg to move the just-suspended process to the background (letting it continue to run) or fg to bring it back to the foreground.

Pressing Ctrl+Z sends the TSTP signal to your process. This halts execution (the kernel won't schedule any more CPU time to the process) and the process is awaiting a CONT to continue processing.

You can emulate/replicate this via kill -TSTP and kill -CONT (since kill will send a nominated signal to your process, despite the name!)

The shell has the functionality to 'background' the process, but this is a relationship between the shell and the process. The process itself doesn't really have the concept of 'background' or 'foreground'.

See here for more info.

Consider this command, which takes approx. 4.5 seconds on my laptop:

echo 2^10000000 | bc -lq | wc -c

When you press Ctrl+Z, the calculation will be suspended. You have an option to resume calculation in foreground using fg, or resume it in background using bg. The latter is more or less equivalent to executing:

echo 2^10000000 | bc -lq | wc -c &