Normal house and job-site debris is fine. The limits come from New Jersey law and from what the receiving facility will take off the truck.
New Jersey keeps televisions and computers out of regular trash. That covers desktops, laptops, and monitors, and it has been the rule statewide since 2011. The state's electronics law points those items to a recycling drop-off instead, so pull them out before the container arrives. Phones, DVD players, and game consoles aren't covered by the ban.
Hazardous material is out as well: paint, solvents, fuel, motor oil, pool chemicals, wet batteries, propane tanks, and anything with asbestos in it. Liquids of any kind are a problem, because a leaking container can be refused at the gate and can put you on the hook for the cleanup.
Appliances and tires need their own handling. Hackensack picks up metal items and appliances only by appointment, for a $10.00 fee, and curbside collection is capped at two furniture items or two bags per pickup. That cap is the main reason a cleanout usually calls for a container.
Not sure about one odd item? Ask your account manager before it goes in, not after.