Are raw scores (?) that have been transformed or translated
  (tests will provide conversion tables)
 

There are several types:
      -61 correct on math subtest = T score of 43)
      -12 correct on the vocabulary section = z score of -.90
      -109 correct as a total test score = 6th stanine
      -142 correct on WizKid Intelligence Scale = IQ of 122 (SD = 16)
 

In general, they allow us to compare:
     -raw scores for kids of different ages (and other demographics...even on different reading tests)
     -the performance of one youngster on different tests/subtests
 

?How can they arrange for this comparison happen?
     -Force scores (using statistical manipulation) into a normal curve
     -Arrange scores so they fall in a normal distribution with same:
      -mean (X)
      -standard deviation (S or SD)
 

Take out your "normal curve" graphic and answer these questions:
     -A student with an IQ of 84 would be how many SD from the mean?
     -If a youngster's score falls into the 98th percentile, in which stanine does it fall?
     -What's the z score of a student who scores an age equivalent of 12-4?
     -Compare SD with z scores, T scores, and stanines.  What is their  relationship?  What do they all try to convey or explain?
            (They are different ways of showing what?)
 

Tom McIntyre at www.BehaviorAdvisor.com