This program uses nested for loop to print powers of numbers from one to twenty. This program is a simple example of using nested loops in Python to perform a repetitive task, in this case computing and printing the values of number powers from 1 to 5 of numbers from1 to 20. Outer for loop iterate over numbers from 1 to 20 by using range function. Inner loop iterate over powers the number is being raised to, i.e. from 1 to 5.

Python Code:

for i in range(1,21):
  for j in range(1,6):
    print(str(i)+"^"+str(j)+"="+str(i**j))

This code uses nested for loops to compute and print the values of i raised to the power of j for all values of i from 1 to 20 and all values of j from 1 to 5.

1. The first for loop sets up a loop that will iterate through the values of i from 1 to 20, inclusive. This is done using the range() function, which creates a sequence of numbers from the starting value (1) to the ending value (20) with a step size of 1.
   
2. The second for loop is nested inside the first for loop, and sets up a loop that will iterate through the values of j from 1 to 5, inclusive. This is also done using the range() function.
   
3. Inside the nested loops, the print() function is called, which will print the result of raising i to the power of j. The str() function is used to convert the integer values of i and j to strings so that they can be concatenated with the other strings. The + operator is used to concatenate the strings together, and the ** operator is used to raise i to the power of j.
   
4. The output of each iteration of the nested loops is printed to the console as a separate line. Each line of output represents the value of i raised to the power of j for a particular combination of i and j.