What is the significance of an IQ score of 68 in Flowers for Algernon?

It shows that Charlie's intelligence is very, very low. Let's see why:

Toward the very beginning of the story, long before Charlie has his operation to raise his intelligence, we find out that he has an IQ score of 68 but also that he's motivated to learn:

"Dr Strauss said I had something that was very good. He said I had a good motor-vation. I never even knew I had that. I felt proud when he said that not every body with an eye-q of 68 had that thing. I dont know what it is or where I got it..."

Scientists disagree vociferously about whether or not IQ tests are valid measures of someone's intelligence, but all we need is some basic information to help understand Charlie's score of 68 and how it relates to the story.

IQ stands for "intelligence quotient" and is a measure of someone's general intelligence. The doctors in the story determined Charlie's IQ by giving him a test and calculating the results.

Please take a look at this diagram as you read through the explanation of it below.

Someone with perfectly average intelligence has an IQ score of 100. And the great majority of people (68% of the population) have a score hovering around that figure, specifically between 85 and 115. If your score falls in that range, we'd say you're of average intelligence.

A significant chunk of people (14% of the population) have scores between 70 and 85, so these are folks you'd call "below average" in intelligence.

Likewise, a significant chunk of people (14% of the population) have scores between 115 and 130, so these are the folks you'd call "above average" in intelligence.

Then, off to one end of the spectrum is a small group of extremely intelligent people with a score over 130 (about 2% of the population) and, likewise on the other end, there are the people we'd say are extremely lacking in intelligence with a score below 70 (again, just about 2% of the population.)

The fact that Charlie's score is below 70, then, reveals that his intelligence is very, very low. It's a significant disability for him.