Some machines have complex processor instructions that can do the same job as a loop with a simple body. For example, x86 processors have an instruction scasb instruction that searches for a byte value; the C strlen function, which searches for a null byte and can be written in C as
while (*p != 0) p++;
can be written in x86 assembly as
repne scasb
Another example is bit counting. Many processors have instructions to do things like finding the number of bits that are set in a word, or finding the index of the lowest-order set bit in a word. However, most programming languages have no operator or function for that, so the programmer has to write a loop like
bit_count = 0;
while (n != 0) {
if (n & 1) ++bit_count;
n = n >> 1;
}
whereas recent x86_64 processors have an instruction for that:
popcnt
Your textbook seems somewhat dated to me. Loop instructions hard-wired in processors are a very CISC feature that most modern processors don't have, the notable exception being the x86 architecture where it is implemented in microcode for backward compatibility. Compilers have become better at understanding what a piece of code including a simple loop does, and converting them to optimized machine instructions. The statement “Compilers, in most cases, cannot determine that a program loop can be replaced by a single instruction” is not always true for 21st century compilers. It is sometimes true; for example I can't seem to get GCC to recognize my naive popcnt implementation above.