Apartment complexes verify your employment and income as a risk assessment. Apartments are expensive and there is a lot of potential for damage to the property or not being able to collect rent, both of which could be financially draining to a business.
Verifying employment and income is a common part of the application process. Communities want to be assured that there's enough income for the applicant to pay for the unit they are renting. Typically they'll use a ratio of three to one, in other words, your income has to be at least three times the rental amount of the unit you are wanting to lease. There are some variations in that, some properties require a four to one ratio, and some are a bit more lenient and only require a tenant to earn two times the rent.
Generally a paycheck stub or a couple of paycheck stubs will serve as proof to an apartment complex that you earn enough to pay for the apartment. If you do not have a paycheck stub, you can submit bank statements to prove income. If you are just starting a new job or haven't worked for an employer long enough to get a paycheck, a letter from an employer can be submitted as proof of income. The property manager may also accept a bank account balance that shows enough money in deposit to pay the lease off.
If you are self-employed, two years of tax returns often suffice. Students may have a trickier time showing that they earn enough to pay for the apartment. In that case, students can generally qualify with a cosigner, usually one of their parents.