How garbage values are assigned to variables in c

Does it mean C first allocates memory to variable 'a' and then what ever there is at that memory location becomes value of 'a'? or something else?

Correct. It is worth mentioning that the "allocation" of automatic variables such as int a is virtually nonexistent, since those variables are stored on the stack or in a CPU register. For variables stored on the stack, "allocation" is performed when the function is called, and boils down to an instruction that moves the stack pointer by a fixed offset calculated at compile time (the combined storage of all local variables used by the function, rounded to proper alignment).

The initial value of variables assigned to CPU registers is the previous contents of the register. Because of this difference (register vs. memory) it sometimes happens that programs that worked correctly when compiled without optimization start breaking when compiled with optimization turned on. The uninitialized variables, previously pointing to the location that happened to be zero-initialized, now contain values from previous uses of the same register.

Does it mean C first allocates memory to variable 'a' and then what ever there is at that memory location becomes value of 'a'?

Exactly!

Basically, C doesn't do anything you don't tell it to. That's both its strength and its weakness.