Let's take a math story problem.
Give an upper class white kid a problem involving tennis scores, no problem. The kid will be able to easily understand what is being talked about, there isn't anything mentally jarring going on.
Give a poor black kid a problem involving tennis scores, boom, problem. Odds of a poor black kid knowing how tennis scoring works, much less likely.
My, largely well to do, neighborhood has tennis courts. The more diverse, and poorer, neighborhood I grew up in, didn't. I am still not sure how tennis is scored, but I am pretty sure the kids in the house next to me understand it.
Repeat this idea a few times with some of the other tests. Give some word recall lists using words poor/minority kids aren't accustom to. It is harder to recall words that you have never heard before, they are basically nonsense syllables, which is a very different test. If you had thrown "quiche" in the middle of a word list 8 year old me would have had no idea what you were talking about.
Modern day IQ tests have tried to correct for these biases, but school administrators can choose an "older" test to purposefully get biased results.