What is a credit check?
Bringing on a new tenant is always a risk for landlords, and one way they assess this risk is through a Credit Check. By "running your credit", a landlord is getting a credit score, which is a number between 300 and 850 that represents how likely you are to pay your bills on time. There are three credit bureaus that determine your score, and they all have different formulas, but your landlord will likely pick the middle score. So if you get scores of 690, 710, and 730 - they'll go with 710.
What's a bad score?
Anything under 700 will concern most landlords; they might reject you or require that you pay a few months rent upfront, or pay more months as a security deposit, to minimize the risk that you don't pay your rent on time.
Get a free credit report. Note: You cannot submit your own report when you apply for an apartment. However, it may help you to determine where you stand before you begin your search.