You've asked great questions and received great replies above.
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What does IQ score really get you?
IQ score gets a bit of self-knowledge. It provides a snapshot measure of intelligence... and in this context, sometimes "less is more," which is to say that the optimal IQ is NOT the highest IQ, but is generally considered to be about 120-125. There are many references to this found online, this old post includes one.

What is the IQ score that translates to a defined success in the eyes of people in these coveted programs?
An IQ score is not one's success index. It is indicative of fluid reasoning + crystallized intelligence.

The DYS program may be coveted because children and families need the services being offered/provided. Therefore it is not a "success," achievement, or accomplishment to be admitted into the program, but rather a "relief" for a child/family to have potential to be among other outlier peers who may tend to encounter similar life experiences (including inadequate educational placement, and societal myths and misconceptions about being gifted or high-IQ).

Davidson... Why 145 and not 135 or 115?
It is my understanding that the aim of the Davidsons was to identify and assist the under-served population of profoundly gifted students.
Originally Posted by About
Oftentimes profoundly intelligent young people are not properly identified and, thus, do not receive an appropriately challenging education. Research shows this can lead to underachievement or even dropping out of school – studies indicate that 40 percent of all gifted students may be underachievers (Handbook of Gifted Education, p. 424).
Is my son an outlier in what he accomplished given a 124 IQ score or is this common?
As mentioned above, 120-125 may be considered the optimal IQ. (This research mentions 125-155, measured on an older IQ test score scale... more info on comparative IQ scores from various tests, here.)
According to this chart, an IQ score of 124 may be found once in about 18 persons.
A teacher with a class size of 25 pupils may encounter such a student once each year.
By comparison, an IQ score of 145 may be found about once in 741 persons.
A teacher with a class size of 25 pupils may encounter such a student once in 30 years; just once in his/her career.

Links to information on IQ score, which may be of interest:
- Hoagies Gifted Education Page - Moderately - Highly - Exceptionally - Profoundly
- Hoagies Gifted Education Page - Underserved

What does a score of 145 translate to in the real world...?
In terms of rarity - IQ score comparison site
In terms of characteristics of profoundly gifted - list, Davidson article
In terms of likely need for support - SENG, founded to meet a need
In terms of likely need for educational advocacy - oobleck
In terms of achievement, success - ???