When a landlord does a background check on tenants they're looking for things such as criminal history and criminal background checks, credit checks, eviction and court records, employment history and rental histories.
Sometimes landlords may do the background checks themselves however some landlords pay and hire tenant screening companies to perform the tenant background checks.
The landlord wants to make sure they get a good tenant so that's why most good landlords will do a good background check and credit check on their potential tenants.
If you have a good clean history and good credit score then you'll likely be able to rent the apartment or house with no problem.
You should then hear back from the landlord within 24 to 72 hours if you've been accepted as a tenant.