Infinite Loops are those program constructs where in there is no break statement so as to get out of the loop, it just keeps looping over the statements within the block defined.
Example:
While(Boolean True) OR for(;;);
{
//Code
}
Embedded systems need infinite loops for repeatedly processing/monitoring the state of the program. One example could be the case of a program state continuously being checked for any exceptional errors that might just occur during run time such as memory outage or divide by zero etc.,
For e.g. Customer care Telephone systems where in a pre-recorded audio file is played in case the dialer is put on hold..
Also circuits being responsible for indicating that a particular component is active/alive during its operation by means of LED's.