In short, the difference between accredited and non-accredited investors comes down to a person's net worth, and annual income.
According to the SEC, an accredited investor must fulfill at least of the following requirements:
Has a net worth over $1 million (excluding the person’s primary residence).
Have an annual earned income of $200,000+ (or a joint income with a spouse of more than $300,000) for the last two years and are expecting their income to be same or more this next year.
Only about 1 in 10 US households qualify as an accredited investor.
A non-accredited investor on the other hand is an investor who doesn't meet any of the requirements listed above, which is about 90% of US households.